You can now require a successful deployment of a branch before its pull request can be merged. This is made possible by a new branch protection setting titled Require deployments to succeed before merging. To enable the setting, create a new branch protection rule for the target branch. Then, select the environments where deployments must succeed before a pull request can be merged, shown here:
This will allow you to ensure code is, for example, exercised in a staging or test environment before it's merged to your main branch.