Is this Children of Amarid (1998) by David B. Coe, the first book in the Lon Tobyn Chronicle trilogy...?
The plot involves an order of mages with hawk familiars, and the cover of the first book does have a light blue background. The antagonist is apparently a former member of the order who was expelled for abusing his power.
A thousand years ago in Tobyn-Ser, Amarid and Theron discovered magical crystals that enabled them to bond with hawks to produce powerful magic. together, they started an order, dedicating themselves to using their powers to help their people. Theron was expelled from the Order for abusing his power, but ever since, the Children of Amarid have faithfully upheld their vow using their power selflessly to protect the land and its people.
Now the idyllic peace of Tobyn-Ser has been shattered by news of mages destroying crops, burning villages, and murdering innocents. Rumor even say that Theron may have returned from the dead to wreak vengeance on Tobyn-Ser an the Order that spurned him.
uncovering the truth about the renegade mages and restoring peace to the sundered land will take a young but powerful Hawk-Mage named Jaryd across the length and breadth of Tobyn-Ser, a journey he must complete before it's too late to save the Order...and the world.
In a blog, the author of the book commented on the "psychic bond" between the mages and their avian familiars.
The mages in my LonTobyn books draw their magic from avian familiars -- birds of prey with whom they share a psychic bond. This bond allows them to draw on the power within the birds to heal, to do battle and protect themselves, and to cast a host of other spells. The birds themselves are characters in the stories, and to this day people who can’t remember any of the titles will talk to me about how much they loved the books by saying “You know: the ones with the hawks and owls.”