Man carrying tune, finally going for a song (5)
I believe the answer is:
cheap
'going for a song' is the definition.
(old-fashioned phrase meaning 'cheap')
'man carrying tune finally' is the wordplay.
'man' becomes 'chap' (I've seen this in other clues**).
'carrying' indicates putting letters inside.
'finally' says to take the final letters.
The last letter of 'tune' is 'e'.
'chap' enclosing 'e' is 'CHEAP'.
(Other definitions for cheap that I've seen before include "A snip" , "Contemptible" , "Economical - rubbishy" , "Shoddy" , "Mean" .)