While it might seem like a logical formation from the adjective "existing," it's not a word that's commonly used or recognized.
If you want to express the idea of "in an existing way," you can use other adverbs like:
* Currently
* Presently
* Already
* Previously
* Actually
For example:
* "The building is currently occupied."
* "The rules are already in place."
* "The project was previously completed."