That woman at supermarket has Covid; initially family shields like this (8)
I believe the answer is:
heraldic
'family shields like this' is the definition.
(as in heraldry)
'that woman at supermarket has covid initially' is the wordplay.
'that woman' becomes 'her' (her refers to a woman).
'at' says to put letters next to each other.
'supermarket' becomes 'aldi' (German supermarket also operating in the UK).
'has' says to put letters next to each other.
'initially' indicates taking the first letters.
The first letter of 'covid' is 'c'.
'her'+'aldi'+'c'='HERALDIC'
(Other definitions for heraldic that I've seen before include "Of family crests" , "show of arms" , "related to genealogical study" , "Of armorial bearings" , "Relating to officers who register genealogies" .)