How do I request a new IP address from my DHCP server using Ubuntu Server?

dhclient eth0

To release the current IP address:

$ sudo dhclient -r

To obtain a fresh lease:

$ sudo dhclient 

Another issue I ran in to was that dhclient kept requesting the same IP from the DHCP server. Running the command dhclient -r did not resolve this. Therefore, after reading the man pages more thoroughly, I found that if I edited the file /var/lib/dhcp3/dhclient.leases to remove all lease references to the specific adaptor, in my case eth0. Then running sudo dhclient eth0 worked as expected and assigned me a new/different IP.

My situation was perhaps unique, but it required that my server pull an address from a higher range than was previously issued. The DHCP server was configured to do this, unless a specific IP address was requested regardless of the range. Since dhclient was specifically requesting the old IP address, based on the information in the dhclient.leases file, the DHCP server was always returning the same address.