If avatar Aang is the last avatar when he dies how can there ever be a new avatar?

Answer 1

He's not the last Avatar, he's The Last Airbender.

He is the last airbender. The Avatar's soul is reincarnated into the next bender in the cycle, so if he were to die, the Avatar would be reborn into the next cycle. As the cycle is air, water, earth, fire, he would be reborn into one of the water tribes. However, as Avatar Roku tells Aang in the Avatar State, the first episode of the second season, "If the Avatar is killed while he is in the Avatar State the cycle will be broken, and the Avatar will cease to exist." As Aang is killed in the Avatar State in "The Crossroads of Destiny," the Avatar Cycle has likely been broken. Indeed, Aang reveals in the third season that he can no longer travel to the Avatar State, which indicates that he is not only the last airbender, but possibly the last Avatar as well.

But then he does manage to go into the Avatar State in the finale and everything is happy. Yay.

Answer 2

Actually, the cycle might be broken. If Aang is the last airbender, the Avatar cycle might not repeat itself once the Avatar must be an airbender again. Unless somewhere else there are Aibenders that are unknow, a female flying bison that could repopulate and reteach people the art of airbending, or Aang leaves a written record of how to Airbend, the cycle will be broken and there will be no more Avatar.

P.S. Aang is not the last avatar, simply the last airbender.