As you mentioned a router, if a (long) power off does not clear the DHCP Lease Table probably a reset of the device would (which I would not do - as you will have to setup from scratch).
Another way to get a new DHCP address would be to reserve the IP of the device you want to test with a non-existent MAC address.
You could also check if you can set the lease time on your router in the DHCP settings and shorten it to a time short enough for your testing.
Be aware that a device will probably ask for the same IP it got before (default client behaviour) so you could up ending with reservations again.
If you are able to change the MAC address of the device this could also induce getting a different IP.
Also, you could setup a LAN DHCP server and disable the functionality on your router. That way you would have more control over the DHCP.(long)