@Skewett 

Hi,

I assume that when you connect some laptop/PC via cable directly to EAP's client (with power injector ofc) then the computer is getting an IP address and have the network access?

I guess your TL WR940N router should be connected to the EAP's client on router's WAN port. Then in router's settings you just set it up as standard router, with Dynamic IP on WAN.

Since it will be your 2nd router in network, make sure that it's LAN addresses are different than your main router's. If those are the same, just simply change that in TL WR940N's settings.

If you set it up that way, then you will have double NAT (one on your main router, 2nd one on your TP-Link). If you would like to open some ports on your second network, then you would have to configure port forwarding on the 1st router (just if you need it ofc). That shouldn't affect internet access tho.

Other thing you can do, is to set up your TLWR940N in Access Point mode. Then it should behave as another device in your main network, instead of creating new, separate subnet. Unfortunately, I'm not aware if in that mode the LAN port's of TP-Link can be used for client's connection or the router behaves as WiFi AP only...

Cheers