Fetch crooner over river (5)
I believe the answer is:
bring
'fetch' is the definition.
(I know that fetch is a more specific form of bring)
'crooner over river' is the wordplay.
'crooner' becomes 'Bing' (Bing Crosby).
'over' indicates putting letters inside.
'river' becomes 'r' (abbreviation).
'bing' placed around 'r' is 'BRING'.
(Other definitions for bring that I've seen before include "Escort" , "Transport" , "Contribute" , "Take with you" , "Cause to exist" .)