Snubs English bishop wearing frills (7)
I believe the answer is:
rebuffs
'snubs' is the definition.
('rebuff' can be a synonym of 'snub')
'english bishop wearing frills' is the wordplay.
'english' becomes 'E' (abbreviation).
'bishop' becomes 'B' (abbreviation for bishop in chess).
'wearing' is an insertion indicator.
'frills' becomes 'ruffs' (both are decorative flourishes on a garment).
'e'+'b'='eb'
'eb' going inside 'ruffs' is 'REBUFFS'.
(Other definitions for rebuffs that I've seen before include "Rejects abruptly" , "Checks" , "Rejects outright and bluntly" , "Brushes off" , "Snubs" .)