Crack in rig initially overlooked (4)
I believe the answer is:
quip
'crack' is the definition.
(both can mean a joke)
'rig initially overlooked' is the wordplay.
'rig' becomes 'equip' (both can mean to supply with equipment or gear).
'initially overlooked' means to remove the first letter.
'equip' with its initial letter taken away is 'QUIP'.
'in' is the link.
(Other definitions for quip that I've seen before include "Clever one-liner" , "Funny remark" , "Witty or sarcastic remark" , "Bon mot" , "Wisecrack" .)