"I want the sword. The sword of Godric Gryffindor."
-- Griphook (DH25)
He and the goblin Gornuk were on the run (along with wizards Dirk Cresswell and Ted Tonks), having refused to accept the authority of wizards over goblins at Gringotts after Voldemort and his Death Eaters took control of the Ministry (DH15). Later, Griphook and Dean Thomas are caught by a crew of Snatchers, who also capture Harry, Ron and Hermione and take them all to Malfoy Manor (DH23). The group narrowly escape and then spend time recovering at Shell Cottage (DH23, DH24).
Griphook assisted with the break-in at Gringotts to steal the Hufflepuff cup Horcrux from the Lestrange family vault, where it had been hidden at Lord Voldemort’s request (DH26). Harry had promised to give him the Sword of Gryffindor in exchange for his help (DH25).
Although he did help Harry, Ron and Hermione get into Gringotts, Griphook didn’t trust them to give the Sword back and stole it from Harry during the chaos inside the vault. He then joined with the other Gringotts goblins chasing the intruders (DH26).
Cunning, direct, willing to steal in line with his beliefs about object ownership
Other canon notes and references
He is extremely vocal about goblin rights and, like all goblins, has strong views about the ultimate ownership of goblin-made objects (DH25).
To grip something is to "take firm hold" of an object or "grasp tightly". To hook something can mean to "catch", "steal" or "attract and hold the attention" of an object (Oxford English Dictionary: grip, hook). Both verbs seem appropriate when describing Griphook's attitude and intentions.
In the films, Griphook dies by the hand of Lord Voldemort after he goes into a murderous rampage upon hearing about the theft from the Lestrange's vault. In the book, however, the Gringotts goblin who reports the intruders to Voldemort is unnamed (DH27).
From the Web
Writing by J K Rowling on WizardingWorld (Pottermore): The Sword of Gryffindor
MuggleNet: Five things you should know about Griphook
Harry Potter Wiki: Griphook
WizardingWorld (Pottermore) features: