Actually, there's still urgency when you're immortal. The kinds of fun you can have depend on the era. For example, competitive athletics may soon cease to be a competition of athletes and become a competition of genetic engineers. Being an athlete may soon become less fun or no fun at all. So even if you're immortal you may miss out on opportunities for having fun if you don't hurry up and win the Olympics while they still take place.
Latest Bloggingheads up with Robert Greene, bestselling author of The 48 Laws of Power and most recently The 50th Law ("Fear nothing").
Excellent commentary/summary by Andy McKenzie here.
The most important piece of advice I got from The 50th Law was "always attack before you are ready".