Skimpy swimsuit: object I discarded in favour of nothing (5)
I believe the answer is:
thong
'skimpy swimsuit' is the definition.
(I've seen this in another clue)
'object i discarded in favour of nothing' is the wordplay.
'object' becomes 'Ti' (Ti is an example).
'discarded in' indicates named letters should be taken away.
'favour of nothing' becomes 'hong' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'ti' with 'i' taken away is 't'.
't'+'hong'='THONG'
Can you help me to learn more?
(Other definitions for thong that I've seen before include "Leather strip that forms the flexible part of a whip: excuse for underwear" , "Leather strip fastener" , "Frequently (archaic)" , "Skimpy underwear" , "Pants" .)