DIAGNOSIS You can, but you have to configure the old router correctly or you'll create a rogue DHCP server that breaks everything.
FIX On your old router, first, factory reset it. Connect a computer to it, access its admin page, and do three things: 1) Disable its DHCP server. 2) Give it a static LAN IP address in your Velop's range (e.g., if Velop is 192.168.1.1, set old router to 192.168.1.2). 3) Don't touch its WAN/Internet port. Now, connect one of the old router's LAN ports to a LAN port on your Velop node via an Ethernet cable. The old router's other LAN ports are now safe to use as a switch.
IF THAT DIDN'T WORK If things get messy, just buy a simple, cheap, unmanaged network switch. Plug it into a Velop LAN port, and it'll instantly give you 4-8 more ports with zero configuration. It's the foolproof way.
HEADS UP Never connect the Velop's LAN port to the old router's WAN port. That creates a "double NAT" and will make some devices and games freak out.