This study explores using **Belatacept**, a medication, in people who have had a **heart transplant**. Participants will either get standard treatment with **Tacrolimus** (a medication that lowers the immune system) or a plan that gradually reduces Tacrolimus and adds Belatacept. All participants will also take **CellCept** or **Myfortic** (medicines to prevent rejection) and **corticosteroids** (drugs that reduce inflammation). The main goal is to see if Belatacept is safe and effective in preventing serious transplant rejection events or other complications within 18 months after the transplant. **Key Points:** - The study lasts for 18 months with a gradual change in medication over the first 9 months. - Participants will need to comply with medication and follow-up visits as part of the study. - Those participating may face risks such as immune system changes and must meet specific health criteria. Participants must meet certain health requirements, such as being free of certain infections and willing to use birth control if applicable. This is a chance to contribute to important research that may improve heart transplant outcomes.