Yes - 'despite this concern' is a perfectly grammatical and usable phrase in written English.
You can use it when the context implies that there is some kind of uncertainty, hesitation or apprehension, but that the speaker is choosing to proceed with whatever action or course of action is being discussed nevertheless. Example: Despite this concern, he decided to continue with his plans to move abroad.
Despite this concern from the professional and scientific communities, the NHPA completely re-shaped the discipline.
Despite this concern from industry experts, politicians are keen to push onwards, and not only in America.
Despite this concern and an initial investigation suspecting misconduct, the matter was closed.Walmart is now paying for turning a blind eye to its mess with further allegations in China, India and Brazil.
On the other hand, conservatives may be glad to hear that despite this concern, Americans have a healthy skepticism that government can be trusted to do much about it.
Despite this concern, it is unclear that patients' preprocedure understanding and expectations are aligned with these potential outcomes.
Despite this concern, there is little research on the psychological processes driving reported suicide ideation in at-risk patients.
Despite this, concerns for elephant safety are rising.
Despite this concern-driven analysis, we emphasise that test cases were designed to those particular concerns and hence did not exercise substantial parts of the involved modules.
Despite this, concerns over a wholesale relocation from China would appear overblown, especially taking into account Chinese workers' higher productivity, the comparative sophistication of China's industrial clusters and the country's undoubted capacity to rapidly mobilise and utilise a large amount of workers to meet substantial international orders.
Despite sharing this concern, I am a happy user of Secret and other apps in the space, and want to see them adjust themselves to provide maximum objective good with the least amount of bad.
Despite all this, concerning history, there is legitimate optimism as momentum is building for a global deal.
