I think it's going to be
Brexit
but I'm still stuck on the first one.
1: boar eyes jay on sun = Boris Johnson, 1st letter is B
2: art eye call five tea = Article Fifty, 2nd letter is r
3: tear e's a may(pole) = Theresa May, 3rd letter is e
4: fl(y)(t)ux = flux, 4th letter is x
5: ream+Maine = remain, 5th letter is i
6: mark-ET axe-s = market access, 6th letter is 5t
(Thanks to dcfyj for suggesting Maine, and Lukas Rotter for getting "access", in Sphinx's Lair chat. It turns out BeastlyGerbil was independently finding the latter here while we were discussing it there.)