One common theme is freedom. Both Buckbeak and Sirius have been wronged and are in a fight for their freedom. In many fanfictions, they help each other achieve that freedom, whether it's Sirius using Buckbeak to escape or Buckbeak being freed with Sirius' help.
At first, it might be a bit tentative. Harry has to earn Buckbeak's trust, just like in the original story. But as time goes on, they start to understand each other better. Buckbeak realizes Harry is different from other humans who might harm him, and Harry sees Buckbeak as more than just a magical creature.
One interesting 'Harry and Hermione Buckbeak' fanfiction could be where they take Buckbeak on a secret adventure through the Forbidden Forest. They might discover new magical creatures and have to rely on Buckbeak's strength and their own wits to get out of tricky situations.
One interesting story could be where Hermione takes it upon herself to study Buckbeak's unique behaviors more closely in Hogwarts. She might discover new magical aspects related to his species.
One great Buckbeak and Sirius fanfiction is 'The Flight of Freedom'. It imagines Sirius bonding with Buckbeak during his time on the run. It beautifully depicts how Buckbeak could sense Sirius' innocence and loyalty, and they form an unbreakable bond as they evade the Ministry's capture. It's full of adventure and heartwarming moments.
There might be a fanfiction where Buckbeak plays a crucial role in protecting Hogwarts. He could use his sharp eyes and powerful wings to spot incoming threats before the students and teachers are aware. For example, he might notice a group of Death Eaters approaching and warn the school in time. He could also carry important messages between different parts of the school or even outside of Hogwarts to get help when needed.
For Harry, his friends in Gryffindor could be a bit confused at first. They know Draco is not exactly a friendly character. But overall, it could lead to a more united front against real threats in Hogwarts. The teachers might also take notice. Dumbledore, for instance, would probably be proud of Harry for showing such selfless courage, regardless of who he was saving.
One interesting plot could be Buckbeak helping Harry in a secret mission outside Hogwarts. Maybe they have to find a hidden magical artifact that is crucial for the safety of the wizarding world.
One idea could be that Buckbeak helps Harry in a secret mission in the Forbidden Forest. Maybe there are dark creatures there that only Buckbeak can sense, and his flying ability and sharp eyes are crucial for Harry to complete the mission.
Well, in some 'harry and buckbeak lemon fanfiction', there could be a plot where Harry has to train Buckbeak for a special magical competition. During this training, they form an even deeper bond. And perhaps Buckbeak helps Harry overcome his fear of a certain spell or magical situation by being there for him. It's all about their unique relationship and how it develops in these fictional scenarios.