Erasing mildly abusive word about a Conservative (8)
I believe the answer is:
effacing
'erasing' is the definition.
('efface' can be a synonym of 'erase')
'mildly abusive word about a conservative' is the wordplay.
'mildly abusive word' becomes 'effing' (mild swear word).
'about' means one lot of letters goes inside another.
'conservative' becomes 'C' (UK political abbreviation).
'a'+'c'='ac'
'effing' enclosing 'ac' is 'EFFACING'.
(Other definitions for effacing that I've seen before include "Obliterating, erasing" , "Making oneself inconspicuous" , "Removing" .)