Accordingly, Conservative admires Greek philosopher (8)
I believe the answer is:
socrates
'greek philosopher' is the definition.
(I've seen this before)
'accordingly conservative admires' is the wordplay.
'accordingly' becomes 'so' (synonyms).
'conservative' becomes 'C' (UK political abbreviation).
'admires' becomes 'rates' (I am not sure about this - if you are sure you should believe this answer much more).
'so'+'c'+'rates'='SOCRATES'
Can you help me to learn more?
(Other definitions for socrates that I've seen before include "Wise guy" , "Coarsest one of great Greek philosophers" , "Plato's mentor" , "Philosophical Greek" , "Plato's teacher, d. 399 BC" .)