In reply to petrch:
Not super knowledgeable about Edinburgh as I'm based in Glasgow, but the Uni club seems pretty active (EUMC), and there are a number of good Facebook groups that are also pretty active; Glasgow Climbers, Edinburgh Climbers, Central Belt Trad Collective, Fort William & Glencoe: Climbing Partners & Outdoor Events, Cairngorms: Climbing Partners.
The Scottish climbing scene is great, and feels quite small and close-knit once you get to know people. I've been here less than a year and already often see faces I know popping up at crags all over the country, and climb with many different people.
Living in Edinburgh is pretty great climbing-wise. Though Glasgow has got Dumby, Lomond, Arrochar and its quicker to get to Glencoe, Edinburgh has probably got the better end of the central belt local crags, the east coast weather, and of course theres EICA Ratho. Quite a good scene there too, you'll find partners there in no time.
