Swearing hair’s put up with voguish silver rings (9)
I believe the answer is:
asserting
'swearing hair's' is the definition.
'asserting' can be an answer for 'swearing' ('assert' can be a synonym of 'swear'). I'm not certain of the 'hair's' bit.
'up with voguish silver rings' is the wordplay.
'up with' becomes 'ssert' (I can't explain this - if you can you should give a lot more credence to this answer).
'voguish' becomes 'in'.
'silver' becomes 'Ag' (Ag is the chemical symbol for silver).
'rings' means one lot of letters goes inside another (some letters are ringed or contained by others).
'ssert'+'in'='ssertin'
'ssertin' going inside 'ag' is 'ASSERTING'.
'put' acts as a link.
Can you help me to learn more?
(Other definitions for asserting that I've seen before include "Declaring strongly" , "Stating positively" .)