How can one properly halachikly arrange for a goy to perform work on shabbos/yomtov for his employer who is a yid? For example: the goy receives computer support calls during the week & as well possibly shabbos/yomtov
We are not allowed to hire a gentile to do work for us on shabbos, and even if the gentile did work for us, there is an additional prohibition against benefitting from that work. There are times when a gentile that is contracted to do a job and he chooses on his own to work on shabbos, that it would be permitted, however that heter will not work here because the employer specifically wants him to work on shabbos. Therefore I don’t see any way to halachically arrange this. I would suggest that you do like B&H and other Jewish companies that are simply not open at all on the Sabbath at all. In the merit of keeping the shabbos properly H-shem should send you an abundance of wealth, and prosperity in your business.
Shulchan Aruch 247-1, 276-1, 307-2.