Well, the Republic of Ireland actually pioneered free zones, creating the Shannon free zone in 1959, offering customs, VAT and corp tax exemptions/reductions. Chinese leaders visited multiple times in the 1980s and pretty much copied the concept for Shenzen.
Now though, the rest of Ireland has pretty much the same benefits as the Shannon free zone, so it's not such a big deal anymore.
And overseas territories, no. When the Republic of Ireland became independent in 1921 it was too late, the age of discovery was over, all the territories were already taken. And Northern Ireland isnt an independent country so doesnt have overseas territories of its own.
There is the Isle of Man though in the Irish Sea which is an autonomous zone.