City overwhelmed by Conservative member’s vice (5)
I believe the answer is:
clamp
'vice' is the definition.
(I've seen this before)
'city overwhelmed by conservative member's' is the wordplay.
'city' becomes 'la' (Los Angeles).
'overwhelmed by' means one lot of letters goes inside another (I've seen this in other clues).
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'member' becomes 'mp'.
'c'+'mp'='cmp'
'la' inserted inside 'cmp' is 'CLAMP'.
(Other definitions for clamp that I've seen before include "Big, important" , "stack of bricks" , "that stops one from driving?" , "squeeze" , "Pile of bricks" .)