@G.Pane, there are several possible solutions depending on the devices you use, so for step-by-step instructions one would need much more details of your router, servers, NAS, network requirements, routing policy you want to implement etc.

If you want to use the L2+ switch to route between one network and another one, proceed as follows:

• Create two VLANs for the two networks, e.g. VLAN 10 and 11.
• Assign the switch an IP from the 192.168.10.0/24 nework, e.g. 192.168.10.250. To do so, see https://www.tp-link.com/de/support/faq/2122/
• Set the default gateway for the switch to the router's IP 192.168.10.1 or whatever your router's IP is. See https://www.tp-link.com/us/support/faq/2123/
• Create a VLAN interface for VLAN 11 and assign it an IP from the 192.168.11.0/24 network, e.g. 192.168.11.250.
• Set up a routing protocol or add static network routes for VLAN 11 (192.168.11.0/24) on all devices in VLAN 10 (192.168.10.0/24) which need to communicate with devices in VLAN 11. The next hop will be the switch's VLAN IF 192.168.10.250.
• Set the switch's VLAN IF 192.168.11.250 as the default gateway for the devices in VLAN 11 needing to access devices in VLAN 10.

With this scheme Inter-VLAN routing is done by the switch, while traffic to all unknown destinations will be forwarded to the switch's default gateway (the router).

Another possible solution is to use the router for Inter-VLAN routing. But the router needs to support VLANs and multiple subnets to do so.

G.Pane wrote

About the VLAN, can you explain the settings? It's a 802.1Q VLAN? Tagged or Untagged? Both? What port i need to use for the .10 and the .11?

It depends on the devices you want to connect and the network topology.

If you want to connect standard PCs, servers, routers etc. you use untagged VLANs. Every VLAN is always 802.1Q, there are no other types of VLANs – even Protocol-based VLANs or MAC-based VLANs are 802.1Q. You can use standard VLANs with fixed assignments per port.

I recommend to study the T2600G User's Guide, there are many application examples for almost any use case.

@G.Pane,

first, to use the switch for routing in VLAN 11, all devices of VLAN 11 must be connected to the switch, else Inter-VLAN routing on the switch does not make sense, but should happen on your router instead.

Secondly, the switch setup is screwed up. You have two default routes (0.0.0.0) and two network routes for 192.168.10.0. This can't work.

I guess your existing network and router already use other switches, right? Is the router VLAN-aware? If not, how do you plan to handle the 192.168.11.0 network on the router? Or don't you need Internet on the devices in the 192.168.11.0 network at all? There are just too many unknown things to be able to help you setting up a switch.

I think it is best if you post a plan for the intended network topology first (and please include pictures in your post using the »image« button in the editor when writing the post, do not append them as files).

G.Pane wrote 

I need internet on both LAN.

This is the important point: If you need Internet on both LANs, you need either two routers or a router which can handle two networks.

You could use:

1. two separate »dumb« Internet routers for the 192.168.10 and 192.168.11 networks each,
2. or use one Internet router for both networks if the router is able to handle two networks itself,
3. or use one Internet router for 192.168.10 network and a router between the 192.168.11 and 192.168.10 networks,
4. or use one Internet router for both networks 192.168.10 and 192.168.11 and routing between the networks on the T2600G switch.

Requirements:

Method 1) is the easiest way, but needs two Internet uplinks. Routing between the .10 and .11 networks can be done on the T2600G switch.

Method 2) requires a router which lets you create two network interfaces and can handle Multi-Nets NAT. If it is VLAN-aware, the better.

Methods 3) and 4) need a router which lets you define network routes.

Since you wrote your router doesn't let you change the subnet mask because it is proprietary, it almost certainly does not meet any of the requirements in 2) to 4) above, right?

So, I'm sorry to say that IMO you cannot extend a network which is limited to a single /24 network on the existing Internet router already, except if you add a second router with NAT capabilities between the .10 and .11 networks as a variant of method 3), but then you will have very limited accessibility from the .10 to the .11 network by using port forwarding on the second router for some selected services only.

Maybe another user in this forum has a better idea how to solve this problem better.