I've managed to configure TeamCity to automatically pull the new checked-in changes from GitLab and build it.
Next step I would like that the build status icon in GitLab reflects the build status from TeamCity.
At the moment each build TeamCity builds, GitLab continues to show "build:skipped". As I understand this is because it's not run with Gitlab CI and that my repo misses gitlab-ci.yml. I did setup the TeamCity CI service for the project but it didn't help with anything. Maybe I'm misunderstanding the purpose of this service.
Is there a way to change the default build tracker from GitLab-CI to TeamCity so that I can see the build status from TeamCity in GitLab as well?