"despite existing" is correct and usable in written English.
You can use it to express that something continues to exist, despite other factors. For example: "Despite existing for many years, the restaurant still enjoys a large customer base."
Despite existing restrictions, Iran currently sells around one million barrels of oil per day.
The campaign comes despite existing foreign investment in the United States wireless industry.
Despite existing societal tensions and frustrations, Japan's managerial achievements contain answers to Western management's most pressing problems.
Taiwan shows one way out of this conundrum; despite existing in a state of legal uncertainty, it has thrived.
He also argued that, despite existing judicial procedures, the jury, not the judges, should determine the truth of the articles.
Despite existing vaccines and specific therapies, epidemics of seasonal influenza annually claim 200,000 500,000 lives worldwide.
Despite existing in the shadows of The Sopranos and Entourage and receiving single-year extensions after each season, The Wire has not only survived but thrived.
If terrorists and criminals do still get guns, despite existing gun laws, there is no reason to have gun laws at all.
Iran has refused to suspend its nuclear program despite existing United Nations sanctions and calls by the United States for new, more stringent sanctions.
Commuters must make an active effort to integrate themselves such as signing to a sports club and university societies, despite existing time pressures.
Despite existing guidelines to assess and manage pain, the management of cancer-related pain is often suboptimal with patients often being undertreated.
