、。
I've got plans to meet my uncle tomorrow.
Literal
Tomorrow, uncle [with-と] meet promise [subject-が] exist [explanatory-んだ].
約束がある = 'there is a promise [to do X]' — a common way to say 'I have plans.' 叔父さん with さん adds warmth and respect for the family member. The と marks 'uncle' as the co-participant in the meeting. んだ gives the explanatory 'I'm telling you this because.'