Democrat is vulgar, reportedly, in speech (9)
I believe the answer is:
discourse
'speech' is the definition.
(discourse is a kind of speech)
'democrat is vulgar reportedly' is the wordplay.
'democrat' becomes 'd'.
'vulgar' becomes 'coarse' ('coarse' can be a synonym of 'vulgar').
'reportedly' indicates a 'sounds like' (homophone) clue.
'coarse' is a homophone of 'course'.
'd'+'is'+'course'='DISCOURSE'
'in' is the link.
(Other definitions for discourse that I've seen before include "Written or spoken communication" , "Formal discussion of a topic" , "verbal communication" , "Communication verbally" , "Conversation, dialogue" .)