Look Conservative leader up and find unpleasant smarmy person (5)
I believe the answer is:
creep
'unpleasant smarmy person' is the definition.
(a creep is an unpleasant person)
'look conservative leader up' is the wordplay.
'look' becomes 'peer' (to peer at something is to look at it).
'leader' says to take the initial letters.
'up' is a reversal indicator (in down clue: letters go upwards).
The initial letter of 'conservative' is 'c'.
'peer'+'c'='peerc'
'peerc' reversed gives 'CREEP'.
'and find' is the link.
(Other definitions for creep that I've seen before include "snake" , "Tiptoe" , "Crawl; skulk" , "Move silently and secretly" , "Cringing, unpleasant person (slang)" .)