All right, see me about that donkey (4)
I believe the answer is:
moke
'donkey' is the definition.
(moke is a kind of donkey)
'all right see me about' is the wordplay.
'all right' becomes 'ok' ('ok' can be a synonym of 'all right').
'about' means one lot of letters goes inside another.
'ok' inserted within 'me' is 'MOKE'.
'that' acts as a link.
(Other definitions for moke that I've seen before include "Mule" , "Beast of burden" , "Donkey (slang)" , "cross" .)