Using just he information you provided the answer is no. For two subnets to talk you need a router to connect them. If your server only changed IP, and not subnets then as long as your clients aren't looking via IP address then it is possible to track it. If they use DNS or some sort of name resolution, maybe ARP, then they would obtain a new address either when DNS is updated or when the server broadcasts is new address.

I'm not sure of your overall goal here so this might not help much. You could setup a router to connect the two subnets, or change the subnet mask on the clients to include a broader subnet. Either way tracking the change won't help if you still can't contact it.