Can I get 10 Gbit to my PC without replacing my router?

Maybe, but the wall connection and your provider’s setup are the big unknowns. A 10 Gbit service advertised for the building does not necessarily mean the port in your apartment is 10 Gbit. Check the link speed on a computer connected directly to the wall, using a compatible 10 GbE network adapter.

If the connection works, splitting it between your PC and router generally takes a 10 Gbit Ethernet switch. But the provider may only allow one device or public IP address, so plugging both into a switch might leave one or both without service. Check with the building or provider before buying gear.

Your current router will cap anything passing through its gigabit ports at roughly gigabit speeds. You can bypass it for the PC, but then the PC is directly exposed to the provider-facing network rather than sitting behind your router. I wouldn't treat that as an equivalent setup, especially if you want the PC to share files or devices with your home network.

A router with a 10 Gbit WAN connection and suitable faster LAN ports is the straightforward way to keep the normal routing and Wi-Fi setup. Before spending on that, verify the wall port actually offers 10 Gbit and whether the provider supports a faster connection to a single device.

There are two separate limits here: the physical link speed and the provider’s IP or authentication policy. A 10 Gbit switch can connect a fast PC and your existing router, but it does not turn the router’s gigabit ports into 10 Gbit ports, and it cannot make a provider issue extra IP addresses.

If only one device is allowed, you could use a capable 10 Gbit router as the device connected to the wall, then connect your existing router behind it for Wi-Fi. Whether that arrangement works well depends on the equipment and configuration, so check compatibility first. Also make sure the PC itself has a 10 GbE adapter and enough capacity to use that speed.

Before buying anything, test the wall connection with a 10 GbE adapter if you can borrow one, or ask whoever manages the apartment network what speed that specific port supports. The building may have a 10 Gbit uplink while each unit gets a slower connection.

Also check whether the service needs a particular login or device registration. A direct PC connection can be a useful test, but don't assume that connecting multiple devices through a switch will work.