Musician in north cutting cost (6)
I believe the answer is:
prince
'musician' is the definition.
(US musician)
'north cutting cost' is the wordplay.
'north' becomes 'N' (abbreviation).
'cutting' means one lot of letters goes inside another (some letters cut their way into a word).
'cost' becomes 'price' (the cost or price of something).
'n' placed inside 'price' is 'PRINCE'.
'in' is the link.
(Other definitions for prince that I've seen before include "Monarch's son" , "eg William or Harry" , "He's a royal" , "Pincer movement around the royal" , "Senior male member of a royal family after the sovereign" .)