Man or woman primarily obsessed with one’s jargon (6)
I believe the answer is:
patois
'jargon' is the definition.
(I know that jargon can be written as patois)
'man or woman primarily obsessed with one's' is the wordplay.
'man or woman' becomes 'Pat' (unisex name - Patrick or Patricia).
'primarily' indicates taking the first letters.
'with' says to put letters next to each other.
'one's' becomes 'I's' (Roman numeral).
The initial letter of 'obsessed' is 'o'.
'pat'+'o'+'is'='PATOIS'
(Other definitions for patois that I've seen before include "Form of language" , "manner of speaking" , "A regional dialect of a language" , "Spoken regional dialect" , "Local dialect heard in patios" .)