Considerable criticism gathering round extreme parts of Henry’s life (9)
I believe the answer is:
biography
'life' is the definition.
('biography' can be a synonym of 'life')
'considerable criticism gathering round extreme parts of henry's' is the wordplay.
I cannot really understand how this works, but
'criticism' could be 'rap' (rap is a kind of criticism) and 'rap' is located in the answer.
'round' could be 'o' (round can mean a round object) and 'o' is found within the answer.
'considerable' could be 'big' and 'big' is present in the leftover letters.
'henry' could be 'h' ('H' can be a synonym of 'henry') and 'h' is found within the answer.
A single letter 'y' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...
(Another definition for biography that I've seen is " Life story".)