Theres not been any mention of the 3 new jobs sharing cross-class skills as far as I am aware, so it is currently unknown.

The 3 new jobs will be fully independent of any class and will have their own skills, I would assume there is 2 likely outcomes:

1) The 3 new jobs operate similar to the current jobs and will share cross class skills with 2 other classes (this would make things simple like allowing DRK access Gladiator's provoke, which is necessary to be a tank in any situation that requires tank swapping)

2) The 3 new jobs have no access to any previous class skills and are equipped with their own unique skill set that still allows them to perform to an equal level (Giving DRK its own form of provoke)

My personal opinion is that considering that the cross class skills are quite a tricky balance suspect and as jobs in future not only get more abilities there will be more jobs to share them it then becomes a potential minefield for developers so I would expect them to try and move away from the cross-class skills in future and aim to create more independent jobs that can function efficiently without the need for cross class abilities also allowing Gamepad players to free up space on their Hotbars for the new job specific abilities.