Conservative Party long for ... (5)
I believe the answer is:
crave
'long for' is the definition.
(I've seen this before)
'conservative party' is the wordplay.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'party' becomes 'rave' (I've seen this before).
'c'+'rave'='CRAVE'
(Other definitions for crave that I've seen before include "Pine" , "Powerfully desire" , "Beg; long for" , "Desire strongly" , "Beseech" .)