Carriage for musician's engagement (3)
I believe the answer is:
I believe this is a double definition.
'carriage' is the first definition.
(I know that Gig is a type of carriage)
'musician's engagement' is the second definition.
(I've seen this in another clue)
'for' is the link.
(Other definitions for gig that I've seen before include "Perform live < in boat" , "Live musical performance" , "In pop parlance, a one-night performance" , "One-night stand" , "A one-night engagement for entertainer" .)