Sing with credit, having nothing on (5)
I believe the answer is:
croon
'sing' is the definition.
(crooning is a kind of singing)
'with credit having nothing on' is the wordplay.
'with' says to put letters next to each other.
'credit' becomes 'cr'.
'having nothing' becomes 'o' (I've seen this in other clues).
'cr' next to 'o' is 'cro'.
'cro'+'on'='CROON'
(Other definitions for croon that I've seen before include "Sing like Bing" , "Sing softly" , "Sing with a soft voice" , "Sing in a soft low tone" .)