Song about King Cole, essentially (5)
I believe the answer is:
carol
'song' is the definition.
(carol is a kind of song)
'about king cole essentially' is the wordplay.
'about' becomes 'ca' (abbreviation for 'circa'**).
'king' becomes 'r' (r is abbreviation for rex).
'essentially' says to take the centre.
The central letters of 'cole' are 'ol'.
'ca'+'r'+'ol'='CAROL'
(Other definitions for carol that I've seen before include "Joyful song - woman's name" , "Joyful religious song" , "See 1" , "Joyful hymn" , "sing happily" .)