No, Karl Urban and Keith Urban are not related. While the known country musician Keith is Australian, the actor Karl is from New Zealand.
Karl Urban is a New Zealand actor who came onto the scene following his appearances in TV series such as Xena: Warrior Princess.
Karl Urban has appeared in the second and third instalments of The Lord of the Rings trilogy (The Two Towers and The Return of the King) as Éomer.
Karl Urban appeared as CIA agent William Cooper in Red. In 2017, Karl Urban played Skurge in Thor: Ragnarok.
Karl Urban played the role of Russian Federal Security Service agent Kirill in The Bourne Supremacy and also starred in The Chronicles of Riddick, Star Trek and Doom.
Karl Urban played Dr Leonard “Bones” McCoy in the 2009 film Star Trek. He reprised the role in the 2013 film Star Trek Into Darkness and the 2016 film Star Trek Beyond.