Extremely happy taking part in best classes (6)
I believe the answer is:
phylum
'classes' is the definition.
(biological category containing several classes)
'extremely happy taking part in best' is the wordplay.
'extremely' means to remove the middle letters.
'taking part in' is an insertion indicator.
'best' becomes 'plum' (informal term for best or top-class).
'happy' with its centre taken out is 'hy'.
'hy' inserted inside 'plum' is 'PHYLUM'.
(Other definitions for phylum that I've seen before include "part of the kingdom" , "Selfless attitude" , "Biological group" , "Taxonomic category above class" , "Group of animals" .)