Back last nag, not the first (7)
I believe the answer is:
'back' is the definition.
('endorse' can be a synonym of 'back')
'last nag not the first' is the wordplay.
'last' becomes 'end'.
'nag' becomes 'horse' (I've seen this before).
'not the first' means to remove the first letter.
'horse' with its first letter removed is 'orse'.
(Other definitions for endorse that I've seen before include "Ratify" , "Give support or approval to" , "Support; sanction" , "Back, support" , "Approve of, sign on back as of cheque" .)