ping sweep

You have a machine on the subnet for which you know the MAC address but you don't know what IP address it got after a restart, use nmap and do a ping sweep:

sudo nmap -n -sP 192.168.1.0/24 | grep "00:11:22:33:44"

-n tells nmap not to never do reverse DNS resolution on the active IP address it finds. Makes scanning faster
-sP Only perform a ping scan (host discovery) and prints the results, go no further.