Assuming that the flavor of Unix is staying the same (AIX?) then the operation is fairly simple. Naturally, the Teamcenter envirnment must be taken down before making any changes to the underlaying architecture.
A rough outline:
Modifying TC_DATA is the "secret sauce" that tells Teamcenter how to connect to the database.
NX 11.0.1.mp01 | SW 2016 | TcUA 11.2.3