Go off record covered by Rush (6)
I believe the answer is:
depart
'go off' is the definition.
(thesaurus)
'record covered by rush' is the wordplay.
'record' becomes 'ep'.
'covered by' means one lot of letters goes inside another.
'rush' becomes 'dart' (darting is a kind of rushing).
'ep' going inside 'dart' is 'DEPART'.
(Other definitions for depart that I've seen before include "make tracks" , "Petard (anag.)" , "Leave, vanish" , "Retire from" , "Set out" .)