Stay with idea, oddly, to find underwear (8)
I believe the answer is:
lingerie
'underwear' is the definition.
(lingerie is a kind of underwear)
'stay with idea oddly' is the wordplay.
'stay' becomes 'linger' (lingering is a kind of staying**).
'with' means one lot of letters go next to another.
'oddly' indicates alternate letters.
The alternating letters of 'idea' are 'ie'.
'linger'+'ie'='LINGERIE'
'to find' is the link.
(Other definitions for lingerie that I've seen before include "Women's underwear and nightwear" , "One from W Atlantic island group" , "Slinky undergarments" , "Women's flimsy underwear" , "flimsy stuff" .)