New head splits up followers (9)

I believe the answer is:

adherents

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'followers' is the definition.
(adherent is a kind of follower)

'new head splits up' is the wordplay.
'new' is an anagram indicator.
'splits up' becomes 'rents' ('rent' can be a synonym of 'split'. I am not sure about the 'up' bit.).
'head' anagrammed gives 'adhe'.
'adhe'+'rents'='ADHERENTS'

Can you help me to learn more?

(Other definitions for adherents that I've seen before include "Followers" , "Supporters of neatherds" , "'Supporters, disciples (9)'" , "Supporters of neat herds" .)

I've seen this clue in the Sydney Morning Herald.

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