In order to get access to specialisations, you will need to be level 30, complete all the main story missions, and then complete all the strongholds as well.
As soon as you finish the True Sons stronghold mission at the Capitol Building, the world tier ticks over and you get dumped back into the White House. Simply walk over the Quartermaster and the bench next to where you unlock skills will allow you to manage your specialisations.
(FYI, you can freely switch between them but you can only accumulate points for the active one.)