Are you asking about connecting the AirPort Express to a Wi-Fi network using only a wireless connection?
Or, will the AirPort Express connect to your new router using a permanent wired Ethernet cable connection?
The AirPort Express.....even the "latest version" with two Ethernet ports......was designed more than 10 years ago. As such, it is likely going have to trouble trying to connect to a new router that is using newer Wi-Fi versions....like Wi-Fi 6 for example.....and newer WPA3 Security.
Will the AirPort Express connect using wireless only to your new router's Wi-Fi network?
This is one of those times when you won't know how well.....or even if.....this will work until you try it out in your home.
Will the AirPort Express connect to your new router using a permanent wired Ethernet cable connection? Probably.
If you want to try to set up the Airport Express, hopefully you have a Mac, since AirPort Utility on a Mac is much easier to deal with than AirPort Utility on an iPhone or iPad, or PC.