Mmmmm ....
I think with your question you have to assume that there is no change in the collective pitch with the transition to forward flight.
If that is the case as the induced flow increases ... the rotor efficiency also increases and therefore the TRT also increases.
Certainly as the airspeed of the aircraft increases you could reduce power (if you wished) to the hover TRT value the aircraft would then be flying with the same rotor thrust value but at reduced power (effectively).
