Stays in my place (6)
I believe the answer is:
corset
'stays' is the definition.
(stays can refer to a corset)
'my place' is the wordplay.
'my' becomes 'cor' (both are expressions of surprise).
'place' becomes 'set' (setting is a kind of placing).
'cor'+'set'='CORSET'
'in' is the link.
(Other definitions for corset that I've seen before include "Tight-fitting undergarment" , "Item of underwear" , "Stays" , "Tight bodice" , "Shaping undergarment" .)