An engagement for Joe, at golf (3)
I believe the answer is:
gig
'an engagement' is the definition.
(gig is a kind of engagement)
'joe at golf' is the wordplay.
'joe' becomes 'GI' (GI Joe).
'at' means one lot of letters go next to another.
'golf' becomes 'g' (phonetic alphabet: alpha, bravo, charlie etc.).
'gi'+'g'='GIG'
'for' is the link.
(Other definitions for gig that I've seen before include "Live musical performance" , "A single musical performance - it's a palindrome" , "Small horse-drawn carriage" , "A one-night musical engagement" , "Palindromic one-night engagement" .)