You can use your Time Capsule in your new network in a number of ways. One would be as a NAS device which I believe you are looking to do.
To do so, you would connect the TC to the new router by Ethernet. You would also want to reconfigure the TC as a bridge and disable its wireless radios.
You can do both of these using the AirPort Utility, as follows:
- Run the AirPort Utility.
- Select the TC, and then, select Edit.
- Select the Network tab.
- Change Router Mode to: Off (Bridge Mode)
- Select the Wireless tab.
- Change Network Mode to: Off
- Select Update and allow the TC to restart.