A Study to Assess the Safety and Efficacy of AZD7789 in Participants With Advanced or Metastatic Solid Cancer

Inclusion Criteria: * Must be ≥ 18 years of age * Part A Dose-escalation cohorts and Part B Dose-expansion cohorts B1, B2, B3 and B5: Histologically or cytologically documented Stage IIIB to IV non-small cell lung carcinoma (NSCLC) not amenable to curative surgery or radiation. * Part B Dose-expansion cohort B4: Histologically or cytologically documented advanced or metastatic gastric and gastro-esophageal junction adenocarcinoma (GEJC) not amenable to curative surgery or radiation. * Must have at least one measurable lesion according to Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 * Provision of archival or fresh tumor tissue sample and/or consent to undergo mandatory on-treatment biopsy for participants enrolled in Part A Dose-escalation * Provision of archival tumor tissue sample or fresh tissue sample for Part B Dose-expansion cohorts B1, B2, B3 and B5. Provision of fresh tumor tissue sample and consent to undergo mandatory on-treatment biopsy for cohort B4. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Non-pregnant women and willingness of female participants to avoid pregnancy or male participants willing to avoid fathering children through highly effective methods of contraception * Adequate organ and bone marrow function measured within 28 days prior to first dose * Part A Dose Escalation Additional Inclusion Criteria: * May have squamous or non-squamous NSCLC * Must have received at least one prior line of systemic therapy, of which at least one prior line of therapy contained approved anti-PD-1/PD-L1 * Must have had immune-oncology (IO) acquired or primary resistance * PD-L1 expression \< 1% or ≥ 1% documented * Part B Dose Expansion Cohort B1 and B3 Additional Inclusion Criteria: * May have squamous or non-squamous NSCLC * Must have received at least one prior line of systemic therapy, of which only one prior line of therapy contained approved anti-PD-1/PD-L1 * Must have had IO acquired resistance * PD- L1 expression ≥ 1% documented * Part B Dose Expansion Cohort B2 and B5 Additional Inclusion Criteria: * May have squamous or non-squamous NSCLC * Must not have received prior IO therapy in the first-line setting, but may have received one prior treatment regime of platinum-based chemotherapy * Cohort B2: PD-L1 expression ≥ 50% documented * Cohort B5: PD-L1 expression 1-49% documented * Part B Dose Expansion Cohort B4 Additional Inclusion Criteria: * Must have received at least one but no more than two prior lines of systemic therapy, of which only one prior line of therapy contained an approved anti-PD-1/PD-L1 * Must have had IO acquired resistance * There are no PD-L1 status requirements for this cohort Exclusion Criteria: * Patients with sensitizing epidermal growth factor receptor (EGFR) mutations or anaplastic lymphoma kinase (ALK) fusions. Documented test result is mandatory for participants with non-squamous NSCLC histology. For participants with squamous NSCLC histology, testing is mandatory only if the participant is a never-smoker or in the presence of a mixed histology. * Documented test result for any other known genomic alteration for which a targeted first line therapy is approved per local standard of care (SoC) * Part B Dose-expansion Cohort B4: documented HER2 amplification (unless a SoC including an anti-HER2 therapy has been received); testing is not mandatory if not required per local guidelines. * Unresolved toxicities of ≥ Grade 2 from prior therapy * Any prior ≥ Grade 3 immune-mediated adverse event (imAE) while receiving immunotherapy or any unresolved imAE ≥ Grade 2 * Must not have experienced a toxicity that led to permanent discontinuation of prior immunotherapy * Symptomatic central nervous system (CNS) metastasis or leptomeningeal disease * History of symptomatic and objectively confirmed arterial (including myocardial infarction) or venous thromboembolic event within 6 months prior to the first dose of study intervention, unless participant is on treatment with adequate antithrombotic medication and is considered to be stable by the Investigator. * History of organ transplant or allogenic haematopoietic stem cell transplant * Infectious disease exclusions: Active infection including TB, HIV, hepatitis A, chronic or active hepatitis B, chronic or active hepatitis C, active COVID-19 infection * History of clinically significant arrythmia as judged by the Investigator * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, cardiomyopathy of any etiology, symptomatic congestive heart failure, uncontrolled hypertension, uncontrolled diabetes mellitus, unstable angina pectoris, history of myocardial infarction within the past 6 months, serious chronic gastrointestinal conditions associated with diarrhea, active non infectious skin disease. Part B Dose-expansion Cohort B4, medication-resistant ascites requiring drainage in the last 28 days prior the start of AZD7789 and/or the occurrence of active gastro-intestinal bleeding, as judged by the Investigator. * Active or prior documented autoimmune or inflammatory disorders, including inflammatory bowel disease (eg, colitis or Crohn's disease), diverticulitis (with the exception of diverticulosis), systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome (granulomatosis with polyangiitis), Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc.. Some exceptions have been specified in the protocol * Past medical history of interstitial lung disease (ILD), drug-induced ILD, radiation pneumonitis requiring steroid treatment, or any evidence of clinically active ILD * Major surgical procedure within 28 days prior to the first dose of study intervention or still recovering from prior surgery * Other invasive malignancy within 2 years prior to screening * Congenital long QT syndrome or history of QT prolongation associated with other medications that cannot be changed or discontinued based on a cardiologist assessment * Any previous treatment with anti-TIM-3 therapy in any setting is not permitted. For Part A, Cohorts B1 and B3:treatment with investigational therapy prior to initiation of study treatment except where the most recent line of therapy was investigational agents added to approved anti-PD-1/PD-L1 as part of standard care. Investigational agents may be given as prior lines of therapy (other than the most recent line) and as monotherapy. Where investigational agents are the most recent line of therapy, they must be given in combination with approved anti-PD-1/PD-L1. For Part B Dose-expansion Cohort B4: investigational agents, other than investigational immune checkpoint inhibitors or other IO agents, may be given as any prior lines of therapy. * Current or prior use of immunosuppressive medication within 14 days prior to the first dose of study intervention * Any concurrent chemotherapy, radiotherapy, investigational, biologic, or hormonal therapy for cancer treatment. Concurrent use of hormonal therapy for noncancer-related conditions is acceptable. * Receipt of live attenuated vaccine within 30 days prior to the first dose of study intervention Note: Participants should not receive live vaccine while receiving study intervention and up to 30 days after the last dose of study intervention * Radiotherapy treatment to the lung within ≤ 4 weeks of the first dose of AZD7789. Palliative bone radiotherapy is allowed if ≥ 2 weeks prior to the first dose of AZD7789.