If your elytra in Minecraft has been completely depleted of durability and is no longer functioning, there are a few options to get it back in working order.
Mending Enchantment
One way to repair a broken elytra is by using the Mending enchantment. This special enchantment allows the item to slowly regain durability as you collect experience orbs. Simply equip the elytra and start gathering XP, and it will gradually repair itself over time.
Combining Damaged Elytras
Another method is to combine two damaged elytra together using either an anvil or a grindstone. Placing the two broken elytras in the appropriate slots will merge them into a single repaired item. The anvil method will retain any existing enchantments, while the grindstone will remove them but provide a small XP bonus.
Phantom Membranes
Finally, you can use phantom membranes, which are dropped by the phantom mob, to directly repair your elytra in an anvil. Each membrane will restore 108 durability points, so it may take several to fully repair a depleted elytra.