Simplify[Conjugate[Exp[I h t]], h t \[Element] Reals]
(* E^(-I h t) *)
Simplify can handle this, if the assumption that the exponent is purely imaginary holds.
If Simplify takes too long it's also possible that you could consider an equivalent replacement rule:
Conjugate[Exp[I h t]] /. Conjugate[h t]->h t
However, you'll have to be a bit more careful with this, since the inside term can vary quite a bit based on assumptions, variable ordering, etc.
If you are not certain that $Ht$ is real, then it's not actually necessarily true that $e^{iHt}=e^{-iHt}$.