Bring up leader of school form (4)

I believe the answer is:

spew

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'bring up' is the definition.
(thesaurus)

'leader of school form' is the wordplay.
'leader of' suggests taking the first letters.
'form' becomes 'pew' (I am not sure about this - if you are sure you should believe this answer much more).
The initial letter of 'school' is 's'.
's'+'pew'='SPEW'

Can you help me to learn more?

(Other definitions for spew that I've seen before include "Expel" , "Forcibly eject" , "Vomit (colloq.)" , "Money (slang)" , "Fetch up" .)

I've seen this clue in The Guardian.

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