I strongly doubt a new owner of Gatwick will affect the choice of air traffic services provider. If the new owners do at some point change provider, BAA could have done exactly the same and in any case,
The new owners already employ Nats to run London City so I wouldn't worry and besides that if they did decide to get rid of Nats it would them cost a fortune what with there not being a radar room at the tower for starters. And Nats being as it is at the mo would probably strip the Tower and airfield of it’s equipment and maybe leave the kettle!
I'd expect if you were valid at Gatwick with NATS they'd relocate you to a different (aerodrome) unit.
Possibly ..... but they may just offer you up to the new operator if you agree
However, that is the job security risk going with aerodrome (airport changing providers) but on the flip side, you have much more flexibility if you choose aerodrome over area
The flexibility within Nats it not like it used to be. A move between units can take well in excess of 2 years if at all and that is in both NSL and NERL.