Graduate is backing Conservative cardinal (5)
I believe the answer is:
basic
'cardinal' is the definition.
(I've seen this before)
'graduate is backing conservative' is the wordplay.
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'backing' is a reversal indicator.
'conservative' becomes 'C' (UK political abbreviation).
'is' backwards is 'si'.
'ba'+'si'+'c'='BASIC'
(Other definitions for basic that I've seen before include "Fundamental -- early computer language" , "Radical" , "Cardinal" , "At the simplest level" , "Rudimentary - programming language" .)