Tip of didgeridoo wedged in composer's bum (5)
I believe the answer is:
cadge
'bum' is the definition.
(both can mean to beg someone for something)
'tip of didgeridoo wedged in composer's' is the wordplay.
'tip of' indicates taking the first letters.
'wedged in' indicates putting letters inside.
'composer' becomes 'cage' (I've seen this before).
The initial letter of 'didgeridoo' is 'd'.
'd' going within 'cage' is 'CADGE'.
(Other definitions for cadge that I've seen before include "Go about begging, scrounge" , "Scrounge, sponge" , "Try to get (something) without paying" , "Sponge (eg money)" , "beg" .)