Speech to musical background -- I had to be quick (5)
I believe the answer is:
rapid
'quick' is the definition.
('rapid' can be a synonym of 'quick')
'speech to musical background i had' is the wordplay.
'speech to musical background' becomes 'rap' (rap involves speaking over music).
'i had' becomes 'id' (I'd).
'rap'+'id'='RAPID'
'to be' acts as a link.
(Other definitions for rapid that I've seen before include "Zippy" , "Brisk" , "Moving at speed" , "haste" , "Flying" .)