Lead Conservative into deeper mess? (7)
I believe the answer is:
precede
'lead' is the definition.
(synonyms)
'conservative into deeper mess?' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'into' is an insertion indicator.
'mess?' is an anagram indicator (I've seen 'mess' mean this).
'deeper' with letters rearranged gives 'preede'.
'c' put into 'preede' is 'PRECEDE'.
(Other definitions for precede that I've seen before include "Antedate" , "Come before (something)" , "Lead the way" , "Pave the way" , "Come/go before" .)