You can also assign an IP address to the Pi in its configuration. You just want to not use any addresses the router is handing out since you have two cooks (or more) at that point. What I do is tell the router it can hand out DHCP addresses from a certain range, but for things where it’s nice to have fixed IP addresses (security cams, NAS, PiAware, etc), I just configure them with addresses outside the DHCP range.
Some may want to have their configs in only one place, like the router, so as you noted, the router can also hand out specific IP addresses when it recognizes the device’s MAC address.
@rkpeck - your Pi may just have been assigned a different address, and like @astrodeveloper said, if you consult the device list you can find its new address if the router assigned IPs in a different order than before. The device list will show MACs though and probably won’t convert those to devices. You can cross reference to the Raspberry Pi Foundation here though: https://udger.com/resources/mac-address-vendor-detail?name=raspberry_pi_foundation
Or maybe it was set up with a static IP that had the old first three numbers of the IP. There gets to be a lot more possibilities if that’s the case.
So even if tedious, if you start trying to ssh or use the address in the browser into 192.168.0.2, 192.168.0.3, 192.168.0.4, etc, if it was dynamically assigned, you should find it (2-254) Your network must be pretty stable if you haven’t had an issue finding it before if dynamically assigned.
DHCP leases expire though. It might fix itself when it re-negotiates, or if it’s still hanging on, a reboot can fix it.
If it was initially configured with a static 192.168.1.xxx, you may need to take the SD card to another computer and edit the configuration manually to get it on the right subnet. You can also plug it and your computer back into the old router to get things back where you can talk to the Pi to set it to the right subnet for the new router.
Or, just configure the new router to 192.168.1 to make it back like the old system and reboot everything to force renegotiation.