If you check bags through, you'll be able to take the airside busses (but still have to clear security at T4), otherwise you'll need to take your bags from T3 to T4 via the Elizabeth Line (free between terminals) or Tube (also free, but T4 is one way, so you'll have to to T2/3 to Hatton Cross, cross platforms, then to T4 (if you're doing the same on the return, you can go straight from T4 to T2/3))