Assuage in a way that may foolishly rile a woman (7)
I believe the answer is:
relieve
'assuage in a way that' is the definition.
'relieve' can be an answer for 'assuage' (I've seen this in another clue). I'm not certain of the rest of the definition.
'foolishly rile a woman' is the wordplay.
'foolishly' indicates an anagram.
'a woman' becomes 'Eve' (Eve is an example).
'rile' with letters rearranged gives 'reli'.
'reli'+'eve'='RELIEVE'
'may' is the link.
Can you help me to learn more?
(Other definitions for relieve that I've seen before include "Lighten a burden or raise a seige" , "Free from obligation" , "Take a job over from - bring aid" , "Take over (from) - ease worries (of)" , "Set free" .)