I killed the Ender Dragon and arrived at the end settlement. The only problem is that the final ship is not there with me. Is there any other way to get to the Elytra?
You'll have to look for a new one
There's no such thing as the Enderschiff.
There are several. You just have to find another one
Only 56% of the end cities have a ship. So on average every second.
Means: Just keep looking. With a little luck you will find an end city with a ship.