Cautious — vet one’s vicar? Strange! (12)
I believe the answer is:
conservative
'cautious' is the definition.
(synonyms)
'vet one's vicar? strange' is the wordplay.
'strange' indicates an anagram.
'vet'+'ones'+'vicar'='vetonesvicar'
'vetonesvicar' with letters rearranged gives 'CONSERVATIVE'.
(Other definitions for conservative that I've seen before include "Moderate" , "right-wing?" , "True blue" , "politician" , "square" .)