My greatest dream is to see a final resolution to the territorial dispute with Spain in my lifetime, which in practice would mean them dropping their claim to my country once and for all. I don't want my kids (or their kids) to have to grow up with the same tension and belligerent relationship with their neighbour as I had to.
From a democratic POV, I'd like to see Gib get its own MP and MEP (if we remain in the EU for the latter), as well as for all Gibraltarians to have the automatic right to vote in UK General Elections.
Economically I'd like to see it diversify to other highish-tech service areas apart from just Online Gaming which currently dominates.
For the UK:
I want to see an in-out EU referendum as soon as possible, the people deserve it and whilst I'd personally vote to leave if it was held tomorrow, if the British populace does vote to stay in I'll dedicate myself to making it work and drop my Euroscepticism.
If we do leave I'd want to see a very aggressive pursuance of much closer relationships with the Commonwealth, with a particular focus on the Anglosphere including the US. I'm not parochial about the UK being this totally independent world power of old, I just see more in common and more sense in being aligned with places like Australia and Canada than turning our back on them in favour of European nations as we did when we joined the EU.
I want to see UK Labour return to the Labour of old, and start representing those they were created to represent again, instead of it being run by a metropolitan Islington elite whose only difference from the Tories is that they wear red ties. Labour could capture my heart with things like ending tax evasion/avoidance and being braver about tackling inequality, but they just won't do it until the New Labour crowd die out (if they ever do).