Upstanding City supporter keeps on showing brains (7)
I believe the answer is:
cerebra
'brains' is the definition.
(plural of cerebrum)
'upstanding city supporter keeps on' is the wordplay.
'upstanding' says the letters should be written backwards.
'city' becomes 'EC' (the City of London postcode).
'supporter' becomes 'bra' (a bra gives support to breasts).
'keeps' indicates putting letters inside (inserted letters are kept inside).
'on' becomes 're' (regarding).
'ec' reversed gives 'ce'.
'ce'+'bra'='cebra'
'cebra' enclosing 're' is 'CEREBRA'.
'showing' acts as a link.
(Other definitions for cerebra that I've seen before include "Hemispheres which comprise the principal parts of the brain" , "Brains" .)