Airport time capsule

Yes, but the Time Capsule must connect to the other router using a permanent wired Ethernet cable connection.

Connect the Ethernet cable from one of the LAN <--> Ethernet ports on the Wi-Fi router to the "O" port on the Time Capsule. Make sure that the Time Capsule is configured to operate in Bridge Mode, which Apple calls "Off (Bridge Mode)"

If you no longer need the wireless signal from the Time Capsule, you can turn it off using AirPort Utility.

It all depends on the type of "modem" that you have connected to the Time Capsule. If you have a simple modem.....the kind with only one Ethernet port.....then the maximum speed of the Time Capsule will be in the 300-350 Mbps range.

If your "modem" is actually a modem/router or gateway.....the type of device that most ISPs provide with their service........then the Time Capsule would able to handle signals in the 750-850 Mbps range.

Now.....if the Time Capsule will be located close to another Wi-Fi router, then it would not make any sense to have two devices producing a Wi-Fi signal, and you would want to turn off the Wi-Fi on the Time Capsule in favor of a newer Wi-Fi router.

If the Time Capsule will be located a few rooms away from the other Wi-Fi router, then the Time Capsule could be configured to use the same wireless network name and password as the main router and provide extended coverage.