Generally, you should be looking for an aircraft specific approval.
The TSO ticket signs off on the Standards compliance for the bit of kit but doesn't (quite obviously) look at all the possible combinations of equipment configurations in the possible end aircraft. There is the very real possibility that installation of a new bit of kit might just be incompatible with the existing fitout for one reason or another.
Checking it out is the job of the maintenance/engineering organisation(s) responsible for the particular aircraft.