Bull's neighbour has meal first off (5)
I believe the answer is:
inner
'bull's neighbour' is the definition.
(the inner is next to the bull on an archery target)
'meal first off' is the wordplay.
'meal' becomes 'dinner' (dinner is a kind of meal).
'first off' means to remove the first letter.
'dinner' with its initial letter removed is 'INNER'.
'has' acts as a link.
(Other definitions for inner that I've seen before include "Target next to the bull's-eye on a dart board" , "pretty good shot" , "Target next to bull" , "Central, internal" , "Esoteric" .)