A slightly strange question regarding Protector in UK / international airspace as the answer could be as simple as 'all the things we do with all our other aircraft'. This would include the usual UK defence & deterrence tasks, maritime, maritime counter terrorism, UK counter terrorism, support/training of the Land component, support/training of the Air component, aircrew training, test & development and the list goes on. It could also be called upon to support civil tasks (SAR, disaster relief, counter narcotics etc) but someone will need to pay the bill.
Perhaps we have got used to the 'same-way-different-day' operations of recent years and have grown accustomed to the airspace limitations of Reaper but Protector operations will be different, more responsive and at range. For example, the platform will be capable of flying direct from the UK to Tripoli, provide ISTAR for an extended period, before transiting home. As the platform will form part of our NATO contribution it is also likely to see service on the fringes of Europe.
As a more extreme example it could launch from the UK and fly direct to NY and image a rediculous comb-over getting into a big black car.