Starts to dream up musical title (7)
I believe the answer is:
duchess
'title' is the definition.
(I've seen this before)
'starts to dream up musical' is the wordplay.
'starts to' suggests taking the first letters.
'musical' becomes 'chess' (Benny Andersson and Bjrn Ulvaeus musical).
The initial letters of 'dream up' is 'du'.
'du'+'chess'='DUCHESS'
(Other definitions for duchess that I've seen before include "Female aristocrat" , "Titled lady" , "Great lady" , "Duke's wife" , "Wife of a duke" .)