Ordinary women in support of Andrew? That's essential! (6)
I believe the answer is:
marrow
'essential' is the definition.
(thesaurus)
'ordinary women in support of andrew?' is the wordplay.
'ordinary' becomes 'O' (abbreviation e.g. O-Levels).
'women' becomes 'w' (standard abbreviation).
'in support of' is a charade indicator (letters next to each other) (in a down clue, some letters hold others up).
'andrew?' becomes 'marr' (Andrew Marr).
'o'+'w'='ow'
'ow' after 'marr' is 'MARROW'.
'that's' is the link.
(Other definitions for marrow that I've seen before include "one of two" , "Vegetable - content of a bone" , "The heart" , "Large green vegetable" , "Connective tissue in bones" .)