Anger of the Parisian overcome by poverty (6)
I believe the answer is:
needle
'anger' is the definition.
(I know that needle is a more specific form of the action anger)
'the parisian overcome by poverty' is the wordplay.
'the parisian' becomes 'le' (definite article in French).
'overcome by' is a charade indicator (letters next to each other) (in a down clue, some letters go over others).
'poverty' becomes 'need' (need is a kind of poverty).
'le' after 'need' is 'NEEDLE'.
'of' is the link.
(Other definitions for needle that I've seen before include "See 6" , "Get to" , "Irritate, goad" , "peak" , "Annoy - syringe" .)