Retiring woman of today put out grin (5)
I believe the answer is:
smirk
'grin' is the definition.
(I know that smirk is a type of grin)
'retiring woman of today put out' is the wordplay.
'retiring' says the letters should be written backwards.
'woman of today' becomes 'ms' (I can't justify this - if you can you should give a lot more credence to this answer).
'put out' becomes 'irk' (irk can mean to annoy or put out).
'ms' in reverse letter order is 'sm'.
'sm'+'irk'='SMIRK'
Can you help me to learn more?
(Other definitions for smirk that I've seen before include "Derisive smile" , "Smug look" , "Self-satisfied smile" , "Appear smug" , "Leer" .)