I assume that Time Warner / Spectrum will be installing a modem/router device....which is also known as a gateway.
Whenever you change the modem or modem/router, or change the ISP, you need to reset the AirPort Extreme back to factory default settings and then set it up again once the new modem/router is installed and up and running.
Reset the AirPort Extreme back to default settings by performing a Hard Reset. That would mean powering up the AirPort Extreme for a few minutes, then holding in the reset button on the back of the AirPort Extreme for 7-8 seconds. Release the reset button and allow a full minute for the AirPort Extreme to restart to slow, blinking amber light status.
Connect an Ethernet cable from the WAN "O" port on the AirPort Extreme to one of the four LAN <--> ports on the back of the Spectrum modem/router.
If you are using a Mac to set up the AirPort Extreme, click the WiFi icon at the top of the Mac's screen and then click on AirPort Extreme under the listing of New AirPort Base Station.

If you are using an iPhone or iPad to set up the AirPort Extreme, tap to go to the Home screen, then tap on Settings. Tap on WiFi and tap on AirPort Extreme under the listing of Set Up New Base Station. The example below shows an AirPort Express, but you will see AirPort Extreme on your device.

When you click (or tap) on AirPort Extreme, that will open up Apple's setup "wizard". Follow the prompts to set up the AirPort Extreme to create a network. You can use the same wireless network name and password that you used before, or set up a new wireless network name and new password.
The example below shows an AirPort Express, but you will of course see a picture of your AIrPort Extreme on your screen.
