Depends on the client you are using for DHCP.
# dhclient (most common)
sudo dhclient -r eth0
sudo dhclient -r eth0 && sudo dhclient eth0
# dhcpcd (Arch, Raspberry Pi, etc.)
sudo dhcpcd -k eth0
# NetworkManager (nmcli)
nmcli device disconnect eth0
nmcli device connect eth0
# systemd-networkd
sudo networkctl renew eth0
sudo networkctl reconfigure eth0
# BusyBox / udhcpc (embedded systems)
sudo udhcpc -R -i eth0
