In the new Star Wars movie there is a black stormtrooper, but I thought that all stormtroopers were clones. I have tried to look this up but with no success.
Why are clones no longer used as stormtroopers?
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Clonetroopers were used by the Republic during the Clone Wars, and were all genetic clones of Jango Fett.
The Empire used Stormtroopers, which were made up, at least in part, of non-clones. This is explicitly shown during the show Star Wars: Rebels, where we see recruits working towards becoming Stormtroopers.
In Star Wars Rebels Season 2, the initial encounter with Captain Rex had him remarking that the Emperor had retired the clones. Stormtroopers are now fully birth-born recruits. 13 years would have passed before the first batch of clones was commanded to execute Order 66, another 19 years before the Battle of Yavin, 3 years from then to the Battle of Endor and then 30 years to The Force Awakens. Considering accelerated ageing, the first batch of clones would be 130 years old by then. The Fett clones would all be dead.
As for the reason why clones aren't used anymore? They are expensive. And the original clones weren't willing executors of Order 66 - they are loyal to the Jedi and the Republic but inhibitor chips overrode their natural loyalties. They were then released (Kanan mentioned clones later telling him they had chips in them, that they had no choice. This indicates he encountered clones who snapped out of it and are no longer willing to go on a Jedi killing spree) from control and are clearly traumatic and unhappy over what they were tricked into doing. Not a good idea to keep these kind of guys around to rule your new Empire.
By the time of The Force Awakens, the First Order has access to less resources than before. Cloning had indeed been considered as an option for how to raise a new army of stormtroopers, but ultimately the decision was made to kidnap babies and raise them in a brainwashed environment instead. Not using clones was a conscious decision of the First Order.