Some nasty lessons, each connected with stigma (6)
I believe the answer is:
styles
'stigma' is the definition.
(I know this)
'some nasty lessons each' is the wordplay.
'some' says the answer is hidden in the clue (some parts of the word are used).
'STYLES' is hidden within 'nasty lessons each'.
'connected with' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for styles that I've seen before include "Fashions and trends" , "Distinctive manners" , "where there was a mysterious affair involving Poirot" , "'Fashions, modes (6)'" , "Fashions and manners" .)