Friend [with-と] appointment [subject-が] exists [because-ので] go [must-なくてはなりません].
約束がある ('have a promise/appointment') is the standard way to say you have plans. ~なくてはなりません is a polite 'must' form — literally 'it will not do if [I] do not go.' More formal than ~なきゃ but less stiff than ~なければならない.