You could say "the remainder of the group is leaving Monday" or "those remaining in the group are leaving Monday".

As Makenna Moser said. Also, note that you *could* use “are” in British English (and probably would) — this is called “notional agreement”. Americans would usually use “formal agreement” — i.e., the word “remainder” is singular in form, so it takes a singular verb even though we're referring to multiple people.

Yes Jonathan, As Makenna has written, you cannot use 'remaining' as a noun. The noun version would be 'remainder'.