Route traffic through VPS

I have a local server machine. And I have, as well, a VPS with a domain name and static IP. Is there anyway I can use the VPS as a front interface to route the traffic to my local machine? My local machine has a dynamic IP, so I cannot use it directly to serve. More specifically: I'd like to instantiate a matrix/synapse server locally, and use the VPS IP and domain name to mediate traffic.

First consider using a simpler network design.

Run the application and its database at the hosting provider. Keep the database private, but access the public API over the internet. Matrix auth and protocol messages are intended to have some security in transport.

Although disadvantage in that this needs to be hardened against attacks from the broader internet. Such as running the http parts behind your favorite reverse proxy. Also disadvantage that you need to trust the hosting provider with your data.

Running a private LAN only server on the local hardware remains an option. Perhaps for an additional test environment.

Also implement IPv6, ask for modern IP from your ISP. No excuse for dynamic addressing when you can have as many /48s as you need.