Non-Christian minister’s ties misrepresented in section of media (9)
I believe the answer is:
priestess
'non-christian minister's' is the definition.
(female priest in non-Christian religions)
'ties misrepresented in section of media' is the wordplay.
'misrepresented' is an anagram indicator.
'in' indicates putting letters inside.
'section of media' becomes 'press' (the newspaper industry).
'ties' with letters rearranged gives 'iest'.
'iest' placed inside 'press' is 'PRIESTESS'.
(Other definitions for priestess that I've seen before include "female cleric" , "Female hierophant" , "Vestal virgin perhaps" , "Clergywoman" , "Eg, Vestal virgin" .)