Unexpected detail about Conservative’s local speech (7)
I believe the answer is:
dialect
'local speech' is the definition.
(eg a regional dialect)
'unexpected detail about conservative's' is the wordplay.
'unexpected' is an anagram indicator.
'about' indicates putting letters inside.
'conservative' becomes 'C' (UK political abbreviation).
'detail' anagrammed gives 'dialet'.
'dialet' placed around 'c' is 'DIALECT'.
(Other definitions for dialect that I've seen before include "type of language" , "Regional language form" , "Regional version of a language" , "Talk of the district" , "Vernacular" .)