DynDNS or a similar dynamic IP system would be a solution, yes - though if your VPN system assumes persistent connections it might run into trouble when the IP address changes. It should be able to recover from that, of course, but that could be a disruption.
There would always be delays when the IP changes - DynDNS is not instantaneous, something on the end point periodically talks to the server, which informs the server what the current IP is, so there is that potential latency between when the IP changes and when the next connection is made. In theory that can be minimized by having the DynDNS client watch for DHCP incoming, and contact the server when that happens, though that depends on having the DynDNS client be installed as part of the firewall firmware. Additionally, there is some concern with the DNS time-to-live. To wit, if the DNS server specifies a 5-minute timeout on the DNS, there potentially would still be a 5-minute gap where your VPN would be using stale, cached DNS information which might no longer match the state of affairs.
I'm assuming from your description that there is a static IP on the old location. Is it possible to have the new location connect to the old via VPN, then set a route in your firewall to route everything from the old location destined for the new one through that connection? I'll freely admit that might be problematic, the new campus VPN might not properly translate incoming packets without there being an existing conversation initiated by the new campus,
