Check out the post below, hopefully it can get you pointed in the right direction. Specifically, the third section where I linked to the questline that you’re currently on.
Do you have any other quests in Dalaran that might be phasing him or otherwise keeping him occupied and not in a quest giving mood? Check through your log and either drop or complete any other Dalaran related quests you might have and see if he will give it to you.
Are you doing this on a boosted character by chance?
Also double check that you are in the correct Dalaran (Legion and not Northrend)
If the character in question was a 110/48 boost (or a 50 boost created from a trial character*) the first few quests for Suramar are flagged as complete. If you go into the cave just north of the Meridil flightpath, you can pick up the questline there.
*I’ve seen some reports that characters who use the level 50 boost on a trial character after the pre-patch have the same stuff as the Legion 110/48 boosts unlocked already as well as the normal 50 boost unlocks.
the pally class hall mount is the only calss hall mount that makes people run around off the normal class hall mount grind.
Dont know why, but it is for us.
The best way, i think, to figure out where you are is to hit up the guide on WoWhead. if you have to delete a quest to restart it, at all the information will be there