I very much enjoy alterac valley, until recently I hadn't known much about drek'thar. After going back in time to draenor I met him and also encountered Mulverick. This made me curious about how old Drek'thar is.
I searched around and found this: Drek'thar Cutscene, but it doesn't seem to hold an answer.
There is no definite answer. But given lore, he was around before the legion presence on Draenor. Given Thrall is in his 20s and Drek is indeed a Chieftain, drek is most likely in his 50s at Garrosh Heallscreams Fall.