A new Build Agent license stays valid with any new major TeamCity version released during the license maintenance period (12 months).
To continue upgrading your Build Agents after that period, you will need to renew your Build Agent Upgrade Subscription for $149 per Build Agent/year. If you use TeamCity Enterprise Server, you will also need to renew your Enterprise Server Upgrade Subscription to ensure compatibility of your Build Agents with your Enterprise Server.
Build Agent Subscription renewals commence from the expiration of your previous subscription period, regardless of when the subscription renewal is purchased. Obtaining the new version of TeamCity under Upgrade Subscription automatically terminates your rights to use any of the previous versions.