The ending of the episode leaves it ambiguous as to what happens to him.
From the episode:
(Alexander is practicing with his bat'leth)
ALEXANDER: I've been waiting. Where's K'mtar?
WORF: He had to leave. He was called away.
ALEXANDER: He never said goodbye.
This question suggests that the fake K'mtar went back to his own time, nothing in the episode suggests that this is what happened (other mistakes are made as well, such as Worf's suggestion that K'mtar would find Worf alive in his own time).
I always assumed he went to live out his life as K'mtar.
Is there any information what happened to K'mtar?