It depends on your cruise regime:
LRC: Yes, your TAS and M decrease as you burn fuel.
Constant M number: Tas remain the same regardless of GW.
Optimium/ Economic M number: M and TAS will be reduced as GW decreases.
Constant N1 (not used for jets): As fuel is burned TAS will increase, TAS will also change depending on CG shift. CG moves forward TAS decrease and viceversa.