You would have an automated build using teamcity, however we could use an PR and once they are manually verified and approved we could proceed to merge for master.
Modify the branch specifications +:refs/pull/*/merge
Once you add the some file in the "feature" branch, it would create an build as we are watching this build in the teamcity.
You need to edit the Build Feature and modify the below settings to ensure you have PR for the the build to merge master branch
Once you create a new file in the feature branch, create PR and wait for the build to succeed in the feature branch.
Once the build is successful it will perform checks for the PR and once the changes are fine fo you, you can merge to master.
So you have now all the changes from the branch to be in master. Once you have approved the changes, it will start to build to master.
This is how you can configure teamcity to have an manual approach for merging into master branch.