For Henri I, queen makes taunt (4)
I believe the answer is:
jeer
'taunt' is the definition.
(I know that jeer is a more specific form of the action taunt)
'for henri i queen' is the wordplay.
'for henri i' becomes 'je' ('I' in French, ie for someone called Henri).
'queen' becomes 'ER' (abbreviation for Elizabeth Regina).
'je'+'er'='JEER'
'makes' acts as a link.
(Other definitions for jeer that I've seen before include "Boo" , "Barrack" , "Ridicule noisily" , "Call out derisively" , "Mock - laugh at" .)