Cost to bring in northern musician at one time (6)
I believe the answer is:
prince
'musician at one time' is the definition.
(Prince was a musician)
'cost to bring in northern' is the wordplay.
'cost' becomes 'price' (the cost or price of something).
'to bring in' indicates putting letters inside.
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'price' enclosing 'n' is 'PRINCE'.
(Other definitions for prince that I've seen before include "Sovereign's son" , "Male heir to a throne" , "Canadian province" , "He's a royal" , "Pincer movement around the royal" .)