first question, how high was HMS Ark Royal's hangar deck?
I understand both hanger decks had a useable height of 17ft 6in height. As such the tail fin would probably need to be made foldable.
You'd have to hinge the radome off to the side so it would fit on the deck elevators.
Add the naval strength tail hook and redesign the tail pipe area to delete the thrust reverser gear. This would save some weight and complexity as well as removing a design aspect that would likely be very susceptible to corrosion at sea.
Strengthen the landing gear to handle carrier operations.
The real challenge would be deciding on the launch system to use: bridle or catpult bar on the nose gear leg.
Presuming the Ark Royal we are refering to is the Audacious Class that was decommissioned in the late 70s and scrapped in 1980, all aircraft that launched from it were launched using the bridle system.
Keeping the Tornado and Ark Royal in their real world timelines, the Tornado still in flight testing when the Ark Royal was decommissioned, I see a possible scenario to make things work:
The proposed CVA-01 carrier project of the early 1960s does not get cancelled and the Audacious Class Ark Royal is retired much earlier and one of the new class of carrier is given the Ark Royal name. You'd still need to make all the above listed design modification to the Tornado, but you wouldn't be constricted by Audacious Class' smaller dimensions.
A refit of the carrier could coincide with the entry of the Tornado into British service in 1982, this could allow th bridle launch system to be replaced with a bar launch system. Looking at the Tornado as it is, I can't see potential bridle hook up and hold-back spots where there isn't already somtehing there, the bar launch would make more sense for it.
As the Sea Harrier was introduced in 1978, it's already a factor by the time the Tornado comes along. The Royal Navy can complement the larger CVA-01 with smaller, ski jump equiped carriers for the Sea Harriers to be based from.
This scenario could possibly open "What if" doors for carrier based, Gr.1 standard Tornados to be part of the Falklands War.