Loch Leglean politics is currently dominated by three Covenants: Crun Clach (founded 954), Mac Gruagach (f. 988), and Horsingas (f. 1073). There are over a dozen other covenants of varying size, and over two dozen aonaranan (solitary magi, not attached to an existing covenant).
Horsingas, the youngest of the three, is also the most active. It was founded and exists for one reason: to drive the Normans out of Scotland. (Its original goal was to put Edgar Ætheling on the throne of England after the Norman conquest of 1066, but the bugger had to up and die on them before they could do that). Since Edgar's death in 1126, they have had to settle for making the borderlands uninhabitable for the invaders, by raiding south across Hadrian's Wall and attacking the Norman keeps in the Lowlands. In between skirmishes with the English, they have raided other covenants and aonaranan under the Pact of Crun Clach. It's possible...in fact, it's quite likely that their activities have skirted (if not breached) both the Pact and the Code on occasion. However, the Tribunal's lone Quaesitor, Whitburh Frithowebba is a member of Horsingas, and she's been known to turn a blind eye to Horsingas's activities, giving them a slap on the wrist if they go too far (i.e. if she fears they might get noticed by the Big Boys).
Crun Clach, also located in the lowlands, was the main power in the region before Horsingas was founded. Since then, Horsingas has steadily eroded their power. Of late, most Tribunal-wide conflicts have boiled down to Horsingas vs. Crun Clach. It doesn't help that Crun Clach is not as militaristic as Horsingas, and Crun Clach finds many of Horsingas's activities off-putting.
Mac Gruagach is less a covenant and more of a clan holding. Most of the magi, as well as the hedge wizards and the mortals associated with the covenant, are extended family. They are often courted by both sides because of their influence with some of the other Highlands covenants, but as time goes by and more covenants are founded in Loch Leglean (often to replace ones that have failed for whatever reason), their influence wanes. However, they still have enough political savvy to count as one of the three main factions in tribunal politics.
And finally, although not one of the Big Three, the oldest covenant is Loch Leglean is the Covenant of Loch Leglean itself. Founded by Pralix in 815, the covenant's main raison d'être is to host Tribunal every seven years. While not exactly centrally located, it does have the advantage of history and tradition, as well as a willingness to act as hosts. So far, no-one has made a legitimate effort to take the honour of hosting Tribunal away from Loch Leglean. As an aside, the next Tribunal meeting is scheduled for 1224.