Show former spouse greeting part (7)
I believe the answer is:
exhibit
'show' is the definition.
(I know that exhibit is a more specific form of show)
'former spouse greeting part' is the wordplay.
'former spouse' becomes 'ex' (an ex-spouse).
'greeting' becomes 'hi' (hi is a kind of greeting).
'part' becomes 'bit' (both mean a piece of something).
'ex'+'hi'+'bit'='EXHIBIT'
(Other definitions for exhibit that I've seen before include "Manifest" , "parade" , "Put on display" , "Show - piece of evidence in court" , "Object on formal public display" .)