Think about Conservative on party right (8)
I believe the answer is:
consider
'think about' is the definition.
(to consider something is to think about it)
'conservative on party right' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'party' becomes 'side' (eg a side or party in a contract).
'right' becomes 'r' (common abbreviation).
'c'+'on'+'side'+'r'='CONSIDER'
(Other definitions for consider that I've seen before include "Hold" , "Think about, reflect upon" , "Look at someone or something thoughtfully" , "Reckon, deem" , "Muse, mull over" .)