Harass blighter about to be brought up (6)
I believe the answer is:
pester
'harass' is the definition.
('pester' can be a synonym of 'harass')
'blighter about to be brought up' is the wordplay.
'blighter' becomes 'pest' ('pest' can be a synonym of 'blighter').
'about' becomes 're' (regarding**).
'to be brought up' says the letters should be written in reverse (down clues only).
're' in reverse letter order is 'er'.
'pest'+'er'='PESTER'
(Other definitions for pester that I've seen before include "Annoy with frequent requests" , "Trouble, annoy" , "Importune" , "Harass" , "Annoy persistently" .)