They've only been dating for a few months and already she's 'got her claws into' him! [=she already has control over him]
With budget cuts looming, the government is trying to 'claw back' some of the money it promised to state agencies.
('chiefly Brit') The press has been 'getting its claws into' him. [=has been attacking/criticizing him]
(..) What am l? Head winder? What are you looking at? Look at you. You gonna grow into a big predator, huh? I don't think so. What do you got? You got. . . Iittle patched fur, no teeth, no claws. Your foot is skin-wrap in mulish. What so threatening about you? (..)2002 Ice Age