Show former husband one part of harness (7)
I believe the answer is:
exhibit
'show' is the definition.
(exhibiting is a kind of showing)
'former husband one part of harness' is the wordplay.
'former' becomes 'ex'.
'husband' becomes 'h'.
'one' becomes 'i' (Roman numeral).
'part of harness' becomes 'bit' ('bit' is part of 'harness').
'ex'+'h'+'i'+'bit'='EXHIBIT'
(Other definitions for exhibit that I've seen before include "Give public show, as of paintings" , "Publicly display" , "Item in show" , "Put on show" , "Something shown in public" .)