Boss carries doubly large instrument (5)
I believe the answer is:
cello
'instrument' is the definition.
(cello is a kind of instrument)
'boss carries doubly large' is the wordplay.
'boss' becomes 'CEO' (chief executive officer).
'carries' indicates putting letters inside (inserted letters carried inside).
'doubly' shows that letters should be duplicated.
'large' becomes 'L' (eg in clothes sizes).
'l' duplicated is 'll'.
'ceo' going around 'll' is 'CELLO'.
(Other definitions for cello that I've seen before include "String quartet instrument" , "Played by Rostropovich" , "big fiddle?" , "large-scale fiddle" , "music produced by this?" .)