Weapon that could make a broken rib stick out! (7)
I believe the answer is:
carbine
'weapon' is the definition.
(carbine is a kind of weapon)
'a broken rib stick out' is the wordplay.
'a broken' indicates anagramming the letters.
'stick' becomes 'cane' (cane is a kind of stick).
'out' means one lot of letters goes inside another.
'rib' anagrammed gives 'rbi'.
'rbi' inserted inside 'cane' is 'CARBINE'.
'that could make' is the link.
(Other definitions for carbine that I've seen before include "A short light automatic rifle" , "Light automatic rifle -- nice bra (anag)" .)