My covering had to be head cloth (6)
I believe the answer is:
chador
'be head cloth' is the definition.
(type of Islamic garment)
'my covering had' is the wordplay.
'my' becomes 'cor' (I've seen this in other clues).
'covering' means one lot of letters goes inside another.
'cor' placed around 'had' is 'CHADOR'.
'to' is the link.
(Other definitions for chador that I've seen before include "Women can be covered in this" , "Muslim head-covering" , "Cloak" , "Item put on by Muslim woman" , "Enveloping Muslim garment" .)