Don't allow little woman to provide instrument (5)
I believe the answer is:
banjo
'instrument' is the definition.
(I know that banjo is a type of stringed instrument)
'don't allow little woman' is the wordplay.
'don't allow' becomes 'ban' (I've seen this in other clues).
'little woman' becomes 'Jo' (character from Little Women).
'ban'+'jo'='BANJO'
'to provide' acts as a link.
(Other definitions for banjo that I've seen before include "Stringed instrument of the guitar family" , "Stringed instrument beloved of old minstrel shows" , "Stringed instrument like guitar with round body" , "Instrument with long neck and round body" , "Relative of the guitar" .)