The phrase "despite the possibility" is correct and usable in written English.
You can use this phrase to suggest that something happened even though it was possible that it would not. For example: Despite the possibility of rain, we decided to go on the picnic.
But councillors were not as convinced and voted to defer their decision - despite the possibility of developers going to appeal.
Despite the possibility of their eminent demise, the underdogs have been the Cup challenge's main sources of levity.
Whatever its imperfections — and despite the possibility it might not work — it needs to be approved, quickly.
Some major productions have been scheduled to shoot even after June 30, despite the possibility of a new strike.
HBOS has admitted it is considering the possibility of a counter-offer despite the possibility of a competition investigation.
The majority (85%) said they did not think their financial situation would worsen in the next year, despite the possibility of an interest rate rise.
And, despite the possibility of coming off the bench and playing behind the newly acquired shooting guard Jerry Stackhouse, he could not stay away.
Adam faces a three-match ban if found guilty and, despite the possibility of that punishment being increased, Coates has declared the club's intention to appeal "vigorously".
Despite the possibility that Sabathia could command one of baseball's highest salaries, Shapiro said: "I really am optimistic that we'll be able to keep C. C. here".
Despite the possibility of undue risk-taking, Mr. Greenwald called incentive fees "perfectly O.K. as long as they're on a fulcrum basis," providing equal rewards and penalties.
She took a job in Saudi Arabia, despite the possibility of mistreatment – a risk widely acknowledged in the Filipino community – because her family desperately needed the money.
