Let me state how I think you have this setup
Printer is Ethernet ---------- Ethernet (WL-330GE wireless adapter)
WL-330GE adapter >>>>>> Wireless >>>>>> New Router
Diagram and mode is from
https://www.asus.com/Networking/WL330gE/HelpDesk_Manual/
ASUS WL-330gE user's manual in English
So I think you need to use Ethernet Adapter Mode !
The computer shown would be your printer
As you are using wireless you need to set up the wireless ssid and the wpa or wep encryption to match the new router I am guessing .
in section 4.3 advanced settings in the above manual link from ASUS.
Also the access point has an ip address by default as 192.168.0.1 255.255.255.0 you would have to most likely have 176.16.1.2 and the new router as 176.16.1.1 and the same subnet mask what ever it is maybe it is 255.255.255.0 then make the printer 176.16.1.5 subnet 255.255.255.0 or whatever subnet you use.
Make sure you log into the new router and alter the DHCP server to assign leases from 176.16.1.10 to 176.16.1.254 with same subnet mask.
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