Worth engaging new singer? (6)
I believe the answer is:
prince
'singer?' is the definition.
(US musician)
'worth engaging new' is the wordplay.
'worth' becomes 'price' (price is a kind of worth).
'engaging' means one lot of letters goes inside another.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'price' placed around 'n' is 'PRINCE'.
(Other definitions for prince that I've seen before include "Monarch's son" , "He's a royal" , "Sovereign's son" , "Royal personage" , "Senior male member of a royal family after the sovereign" .)