This Study is a Phase II Study of AZD6738 in Combination With Durvalumab in Patients With Solid Tumor (Cohort A (N=30): GC Who Have Failed Secondary Chemotherapy Treatments Regimen; Cohort B (B=30): Melanoma Patients Who Have Failed to IO)

Inclusion Criteria:

1. Provision of fully informed consent prior to any study specific procedures.
2. Patients must be ≥ 18 years of age
3. Patient with ATM deficient or ATM proficient through IHC. ATM expression status will be assessed prospectively. Minimum numbers of each patient group (ATM proficient and deficient) will be required for analysis, therefore central prospective screening will be deployed to ensure this is achieved.
4. Body weight \>30kg
5. Cohort A: Confirmed histological or cytological diagnosis of gastric adenocarcinoma (including GEJ) that is at an advanced stage and that has progressed following who have failed secondary chemotherapy treatments (confirmed by imaging)
6. Cohort B: Confirmed melanoma (metastatic) who has progressed to prior anti-PD(L)1 therapy (immediate prior regimen)
7. Have the presence of measurable disease as defined by the Response Evaluation Criteria in Solid Tumors (modified RECIST) version 1.1 which is suitable for accurate repeated measurements.
8. Provision of tumor sample (from either a resection or biopsy) for ATM IHC and other exploratory biomarker
9. Patients are willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations.
10. ECOG performance status 0-1 with no deterioration between screening and the first dose of study treatment
11. Patients must have a life expectancy ≥ 3 months from proposed first dose date.
12. Patients must have had a washout period of 3 weeks for any prior therapy prior to the start ot study drug. The following intervals between the end of the prior treatment and first dose of study drug must be observed: ≥ 4 weeks for radiotherapy (patients who receive palliative radiation for nontarget lesions need not have a 4 week washout period and can be enrolled immediately); patients may receive a stable dose of bisphosphonates or denusomab as long as these were started at least 4 weeks prior to treatment; ≥ 4 weeks for major surgery; ≥ 7 days for minor surgical procedures; ≥ 14 days (or 5 half lives whoever is longest) for any investigational product.
13. Patients must have acceptable bone marrow, liver and renal function measured within 28 days prior to administration of study treatment as defined below:

    * Haemoglobin ≥9.0 g/dL (transfusion not permitted within 14 days of study medication)
    * Absolute neutrophil count (ANC) ≥ 1.5 x 109/L
    * INR ≥1.5 or evidence of impaired hepatic synthesis function
    * Platelet count ≥100 x 109/L (transfusion not permitted within 14 days of study medication
    * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN)
    * AST (SGOT)/ALT (SGPT) ≤ 2.5 x institutional upper limit of normal unless liver metastases are present in which case it must be ≤ 5x ULN
    * Serum creatinine ≤1.5 x institutional ULN
    * Glomerular filtration rate \< 45 mL/min as assessed by standard methodology at the investigating centre
    * Haematuria: +++ on microscopy or dipstick
14. Female patients of childbearing potential must have a negative pregnancy test (urine or serum), must not be breastfeeding and using adequate contraceptive measures.

    Female patients must use a highly effective contraceptive measure from screening until 90 days after the last dose of drug. All methods of contraception (except for total abstinence) should be used in combination with the use of a condom by a male sexual partner for intercourse (see Restrictions below).

    Female patients must have evidence of non-childbearing potential by fulfilling one of the following criteria at screening:
    1. Post-menopausal women defined as aged more than 50 years and amenorrhoeic for at least 12 months following cessation of all exogenous hormonal treatment.
    2. Documentation of irreversible surgical sterilisation by hysterectomy, bilateral oophorectomy, or bilateral salpingectomy, but not tubal ligation.
    3. Amenorrhoeic for 12 months and serum follicle-stimulating hormone (FSH), lutenizing hormone (LH) and plasma oestradiol levels in the postmenopausal range for the institution
15. For the duration of the study and for 1 week after the last study drug administration, sexually active male patients must be willing to use barrier contraception i.e. condoms with all sexual partners. Where the sexual partner is a 'women of child-bearing potential' who is not using effective contraception, men must use a condom (with spermicide) during the study and for 6 months after the last dose of a study drug.
16. Mandatory biopsy during the screening window prior to dosing and at progression (fresh frozen will be mandatory if clinically feasible)

Exclusion Criteria:

1. Diagnosis of ataxia telangiectasia.
2. Any previous treatment with ATR inhibitors, DNA -damage repair inhibitors
3. Any gastrointestinal condition that would preclude adequate abosrportion of AZD6738 including but not limited to inability to swallow oral medication, refractory nausea and vomiting, chronic gastrointestinal diseases or previous significant bowel resection, intestinal obstruction or CTCAE grade 3 or grade 4 upper GI bleeding within 4 weeks before the enrollment.
4. Active or prior documented autoimmune or inflammatory disorders (including IBD\[e.g. Chohn's disease, ulcerative colitis or diverticulitis\], SLE, sarcoidosis syndrome, tuberculosis, Wegener syndrome, myasthenia gravis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, history of primary immunodeficiency or HIV infection, known hepatitis B or hepatitis C infection, history of organ transplant that requires use of immunosuppressives, glomerulonephritis, nephritic syndrome, Fanconi Syndrome or renal tubular acidosis within the past 2 years prior to the start of treatment. The following are exceptions to this criterion:

   * Subjects with vitiligo or alopecia, hypothyroidism (eg, following Hashimoto syndrome) stable on hormone replacement or psoriasis not requiring systemic treatment; patients with coeliac disease controlled by diet alone and patients without active disease in the last 5 years may be included after consultation with Chief Investigator.
5. Untreated central nervous system (CNS) metastatic disease, leptomeningeal disease, or cord compression. Note: Subjects previously treated for CNS metastases that are asymptomatic, radiographically and neurologically stable for at least 4 weeks and do not require corticosteroids (of any dose) for symptomatic management for at least 4 weeks prior to the first dose of treatment are not excluded.
6. Patients with second primary cancer, except: adequately treated non-melanoma skin cancer, curatively treated in-situ cancer of the cervix, or other solid tumours curatively treated with no evidence of disease for ≤3 years.
7. Current or prior use of immunosuppressive medication within 4 weeks prior to the first dose of durvalumab, with the exceptions of intranasal, topical, and inhaled corticosteroids; systemic corticosteroids at physiologic doses not to exceed a dose \> 10 mg prednisone / day or equivalent)
8. Patient was in receipt of any live attenuated vaccination within 30 days prior to study entry or within 30 days of receving study therapy.
9. Receiving or having received, concomitant medications, herbal supplements, and/or foods that significantly modulate P450 3A4 (CYP3A4) or Pgp activity (washout periods of 5 half-lives). Note these include common azole antifungals, macrolide antibioics and other medications.
10. Patient with any of the following cardiac criteria:

    * Mean QT interval corrected for heart rate (QTc) ≥ 470 ms calculated from 3 electrograms (ECGs) using Friderecia's correction
    * Any clinciallly important abnormalities in fhythm, conduction or morphology of resting ECG e.g. complete left bundle branch block , third degree heart block, second degree heart block.
    * Any factors that increae the risk of QTc prolongation or risk of arrhythmic events such as heart failure, hypokalaemia, congenital long QT syndrome, family history of long QT syndrome or unexplained sudden death under 40 years of age or concomitant medication known to prolong the QT interval
    * Uncontrolled hypotension: systolic BP \< 90 mmHg and/or diastolic BP 60 mmHg or clinically relvant orthostatic hypotension, including a fall in blood pressure of \> 20 mmHg
    * Atrial fibrillation with a ventricular rate \>100 bpm on ECG at rest
    * Symptomatic heart failure (NYHA grade II-IV)
    * Known reduced LVEF \< 55%
    * Prior or current cardiomyopathy
    * Severe valvular heart disease
    * Uncontrolled angina (Canadian Cardiovascular Society grade II-IV despite medical therapy)
    * Stroke or transient ischaemic attack in the last 6 months prior to screening
    * Acute coronary syndrome within 6 months prior to starting treatment
11. Ophthalmological conditions as follows:Intra-ocular pressure \>21 mmHg, or uncontrolled glaucoma (irrespective of intra-ocular pressure), Current or past history of central serous retinopathy or retinal vein occlusion
12. Any evidence of severe or uncontrolled systemic disease, including active infection (requiring antibiotics, antifungals or antivirals), diabetes type I and II, uncontrolled seizures, bleeding diatheses, severe COPD, severe Parkinson's disease.
13. Any unresolved toxicity NCI CTCAE Grade ≥2 from previous anticancer therapy with the exception of alopecia, vitiligo, Major surgical procedure (as defined by the Investigator) within 28 days prior to the first dose of IP. Note: Local surgery of isolated lesions for palliative intent is acceptable.
14. Female patients who are pregnant or breastfeeding or male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 90 days after the last dose of durvalumab monotherapy.
15. Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients.