It's not easy having a dog in Gibraltar, especially a large one. I have a German shepherd, and I have found it quite difficult. There are lots of people with small dogs though.
Firstly I found it hard to find an apartment to rent which would take large dogs, and it's usually a clause in the terms of the lease that they must not bark or otherwise cause a nuisance.
There are 3 or 4 beaches in Gib where you can take dogs, but only in the winter months between 1st Oct and 1 April (I think those are the right dates). I go down to Europa point before school is out or people finish work, and then I can usually let him have a run off the lead if there's not many people around. This is harder in the summer too, as there's large coach loads of tourists who visit. Nevertheless this usually works out ok for me. There is also a car park round at Catalan Bay beach where I take him in the mornings or late evening, and no-one usually minds if I run him on the beach there. In the summer and particularly in the holidays it's harder, but I just walk him after dark - it's cooler then anyway.
At weekends we go up to Bolonia beach where they officially don't let dogs on the beach but it's quite wild and hippie-like up there, and there's always lots of dogs around. The beach is wonderful and miles long, and he loves going there.
Otherwise you'll just have to walk your dog on the lead most times, make sure you have your doggy poo bags with you, and beware the apes if you walk up on the Rock or the Med steps! You can walk a dog pretty much anywhere on the lead, except in the Alameda Gardens, which is a shame as it's lovely there.
Good luck anyway!