Rushing off, the ingrate! (7)
I believe the answer is:
tearing
'rushing' is the definition.
(tearing is a kind of rushing)
'off the ingrate' is the wordplay.
'off' indicates an anagram.
'ingrate' anagrammed gives 'TEARING'.
(Other definitions for tearing that I've seen before include "violent" , "Granite (anag.)" , "'Pulling apart, ripping (7)'" , "splitting" .)