Fabric displayed by wife over Irish tweed regularly (7)
I believe the answer is:
worsted
'fabric' is the definition.
(worsted is a kind of fabric)
'wife over irish tweed regularly' is the wordplay.
'wife' becomes 'w'.
'over' becomes 'o' (cricket abbreviation**).
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'irish'+'tweed'='irishtweed'
The alternate letters of 'irishtweed' are 'rsted'.
'w'+'o'+'rsted'='WORSTED'
'displayed by' is the link.
(Other definitions for worsted that I've seen before include "Beaten" , "Fabric made from fine smooth wool yarn" , "Beat" , "taken to the cleaners" , "sort of suit?" .)