Escort, being tipsy, stays (6)
I believe the answer is:
corset
'stays' is the definition.
(stays can refer to a corset)
'escort being tipsy' is the wordplay.
'being tipsy' is an anagram indicator.
'escort' with letters rearranged gives 'CORSET'.
(Other definitions for corset that I've seen before include "Restraining undergarment" , "Stiff supportive undergarment" , "Type of bodice" , "A woman's close-fitting support undergarment" , "Tight bodice" .)