How to change data directory path for existing TeamCity server?
You should stop TeamCity server, move existing TeamCity data directory to a new location, let TeamCity server know about new data directory using /conf/teamcity-startup.properties file (since 9.1 version) or TEAMCITY_DATA_PATH environment variable (for more details see this section). Actually you can use instructions for Copying TeamCity server, but skip Installation and database copy steps.