The woman regularly went to get bed linen (5)
I believe the answer is:
sheet
'bed linen' is the definition.
(sheet is a kind of bed linen)
'the woman regularly went' is the wordplay.
'the woman' becomes 'she' ('she' refers to a woman).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternating letters of 'went' are 'et'.
'she'+'et'='SHEET'
'to get' is the link.
(Other definitions for sheet that I've seen before include "Whence to sing hymns?" , "Piece of paper, linen, or water" , "Page of postage stamps" , "Sail-rope on the bed?" , "Large piece of fabric" .)