Be root or use doas / sodu / whatever, and
/usr/sbin/service dhcpcd restart
If it can't contact the DHCP server, you may have some issue outside the scope of NetBSD. Bad cable, network configuration, etc.
If dhcpcd wasn't running, or you get an error that you should use onestart, you need to add
dhcpcd= YES
to /etc/rc.conf
BTW, now that you've got a server running NetBSD, it might be in your best interest to run your own DHCP server and not use the one in your router. You really want to have as much control over your own stuff as you can, in my opinion.