Symptoms

Currently, JIRA is not able to set permission scheme based on issue type. It is a improvement request being filed in  JRA-5865 - Getting issue details... STATUS . So if we want to allow only certain users to perform a certain transition on specific issue type.

Workaround

For example, if we want to allow only Team Lead to close bug and improvement request in Project A, we can do the follow setup.

1. Create a new Workflow scheme by referring to Configuring workflow schemes - Adding a workflow scheme.
2. Copy the current in-use project A's workflow.
3. In the copied workflow, modify the "close issue" transition > under condition > add a new condition > only allow Team lead group to perform close issue transition. You can refer to Advanced workflow configuration to learn how to set condition to transition.
4. In the new workflow schemes, assign the modified workflow to the scheme by selecting the issue type - bug. Refer to Configuring workflow schemes for detail steps.
5. Repeat step above for improvement request and other issue type.
6. Associate the new workflow scheme to the project.

After that, only users from Team lead group/role are allow to close bug and improvement request, while other issue types are not affected.