Song that's very long cut by half (4)
I believe the answer is:
solo
'song' is the definition.
(I've seen this in another clue)
'very long cut by half' is the wordplay.
'very' becomes 'so' (both can mean 'extremely').
'cut by half' means to take half the letters.
'long' with half the letters taken is 'lo'.
'so'+'lo'='SOLO'
'that's' acts as a link.
(Other definitions for solo that I've seen before include "Alone - card game" , "Unaccompanied passage" , "something for one to do" , "Card game; for one" , "Piece for single performer" .)