Someone chasing a contented response, about to go to law (7)
I believe the answer is:
pursuer
'someone chasing' is the definition.
'a contented response about to go to law' is the wordplay.
'a contented response' becomes 'purr' (contented sound made by a cat).
'about' indicates putting letters inside.
'to go to law' becomes 'sue' (as in suing somebody in court).
'purr' going around 'sue' is 'PURSUER'.
(Other definitions for pursuer that I've seen before include "One following" , "Chaser" , "One giving chase" , "Follower" , "He's hounding" .)