"possibility of improvement" is correct and usable in written English.
You can use it when you are talking about the potential to make something better or to develop something further. For example, "We discussed the possibility of improvement for the current system."
And once humans started thinking about the future, and the possibility of improvement, then everything became possible.
Ideally, his family would prefer him to stay in Qatar until his condition improves or doctors certify there is no possibility of improvement.
It has so many sides, it touches life at so many points, at every one there is such possibility of improvement and excellence.
Mexico's president-elect, Felipe Calderón, visiting Washington, DC, earlier this month, said that the outcome of the election held out the possibility of "improvement" in bilateral ties.
I think there's a very large number of people who normally don't express opinions but who, when they see some possibility of improvement, or someone who seems to offer something different, the lid comes off.
She said she reached her decision to step down over the recent Presidents' Day recess as she weighed the six-year commitment she was making against the severe doubts she has about the possibility of improvement in the Senate any time soon.
Following a questionnaire survey, a series of in-depth interviews was also conducted to explore the possibility of improvements.
The resulting cost of CO2 avoided is 36€/tCO2, equal to the reference case, with large possibility of improvements thanks to the conservative membrane design selected.
Batteries have a significant number of limitations that make them difficult to use in cars, and a large part of the potential for battery-powered vehicles is based on the possibility of improvements in battery technology.
Since this resistance has received little attention in previous studies, further emphasis on the design of drug nanoparticles with more rapid interfacial reaction offers the possibility of improvements in dissolution rates.
The rate at which identified issues were resolved was generally higher in the study group than in the control group, suggesting the possibility of improvements in care quality along measured dimensions and enhanced diffusion of new protocols based on new clinical evidence.
