You have to activate the specialization first. It says so when you select it.
Then do the five tiers of quest for the specialization to be able to start earning specialization points.
Stronghold=5 points
Bounty=3 points
Leveling=3 points
Lvl 4 control point=1 points
Weekly/Daily-give points as well I forget how many.
The 5 quest lines are very dumb, with the buggy state of the game, you may run into a bunch of issues trying to finish them.
Anytime you get stuck just look up a Youtube video and pay attention to the tips/suggestions.
This is another failure by Ubi since it doesn't tell you what to do when you buy the WLNY expansion and level boost.