Belt out maybe with rented vest (7)
I believe the answer is:
singlet
'vest' is the definition.
(synonyms)
'belt out maybe with rented' is the wordplay.
'belt out maybe' becomes 'sing' (I can't justify this - if you can you should give a lot more credence to this answer).
'with' is a charade indicator (letters next to each other).
'rented' becomes 'let' (I've seen this in another clue).
'sing'+'let'='SINGLET'
Can you help me to learn more?
(Other definitions for singlet that I've seen before include "Sleeveless shirt" , "Tingles in vest" , "One unaccompanied" , "Sleeveless vest" , "Sleeveless garment" .)