This study will look at the effects of CagriSema on cardiovascular events (for example heart attack and stroke) in people living with cardiovascular disease. Participants will either get CagriSema or a dummy medicine (also called "placebo") which has no effect on the body. Which treatment participants will get will be decided by chance. Participant's chance of getting CagriSema or placebo is the same. Participants will inject the study medicine once a week. The study medicine will be injected briefly with a thin needle, typically in the stomach, thighs or upper arms. The study will last for up to 4.5 years.

Inclusion Criteria:

• Male or female

• Age above or equal to 55 years at the time of signing informed consent

• Body mass index (BMI) greater than or equal to (>=) 25.0 kilograms per meter square (kg/m^2)

• Established CVD as evidenced by at least one of the following:

  1. Prior myocardial infarction

  2. Prior stroke (ischemic or haemorrhagic stroke)

  3. Symptomatic peripheral arterial disease (PAD) defined as at least one of the following:

     1. Intermittent claudication with an ankle-brachial index (ABI) less than (<) 0.85 at rest
     2. Intermittent claudication with a >= 50% stenosis in a lower extremity peripheral artery documented by X-ray angiography, magnetic resonance (MR) angiography, computed tomography (CT) angiography or Doppler ultrasound
     3. Prior revascularization procedure of a lower extremity peripheral artery
     4. Lower extremity amputation at or above ankle due to atherosclerotic disease (excluding e.g., trauma or osteomyelitis)

For participants with T2D at screening the following inclusion criteria also apply:

• Diagnosed with type 2 diabetes mellitus (T2D) >= 180 days before screening

• HbA1c 6.5%-10% (47-86 millimoles per mole [mmol/mol]) (both inclusive), as measured by central laboratory at screening

• Treatment with either:

  1. Lifestyle intervention alone
  2. 1-3 marketed oral antidiabetic drugs (OADs) (metformin, α-glucosidase inhibitors (AGI), glinides, sodium-glucose co-transporter 2 inhibitor (SGLT2i), dipeptidyl peptidase 4 (DPP4)-inhibitors, thiazolidinediones, or sulphonylureas (SU) as a single agent or in combination) according to local label
  3. Basal insulin alone or in combination with up to two marketed OADs, all according to local label

Exclusion Criteria:

• Myocardial infarction, stroke, hospitalization for unstable angina pectoris or transient ischaemic attack within 60 days before screening
• Planned coronary, carotid or peripheral artery revascularisation known on the day of screening
• Heart failure classified as being in New York Heart Association (NYHA) Class IV at screening
• Treatment with any glucagon-like peptide-1 (GLP-1) receptor agonist (RA) or a medication with GLP-1 activity within 90 days before screening
• End stage renal disease defined as estimated glomerular filtration rate (eGFR) < 15 millileters per minutes per 1.73^2 (mL/min/1.73 m^2), as measured by the central laboratory at screening
• Chronic or intermittent haemodialysis or peritoneal dialysis

According to the Novo Nordisk disclosure commitment on novonordisk-trials.com