In case of giving three clear divorces, the wife becomes divorced with mughallaza bayinah, the marital relation between the spouse shall come to a complete end. Having passed her iddah, she can marry anywhere she likes. She can not marry the first husband without Halalah Shariyah and will no longer remain his wife, so it is haram to keep her as wife, both should live separately now with purdah (like strangers).
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband