"possess quality" is a correct and usable phrase in written English.
It means to have a particular characteristic or trait. Example: "The new car model is known to possess quality features that make it stand out from its competitors."
They possess quality all over the pitch.
"We know they have three lads in behind the strikers who possess quality and let them play and we let them do that.
Computer simulation and laboratory experiments have demonstrated these controller designs possess quality performances, which are comparable with the other designs for the same applications.
So we must ask: What reasons do we have for believing that the fact that persons possess quality X entails that we are morally obligated to respect persons by treating them in certain ways?
These investigations possess quality character for the detection substances which occur in various essential oils.
Women, she thinks, possess qualities advantageous for the job: "When you have kids, you need to be patient," she explained.
The hyperbole of N.B.A. promotions often implies that players can walk on water and that they possess qualities of goodness beyond basketball.
Mrs. Crasthorpe did not interest or concern him, and it was hard to believe that this pushy, over-lively woman might possess qualities more appealing than her manner.
They possess qualities that have effects on the heart, stomach, intestines, and nervous system.
Young people possess qualities that make their active participation in DRR and response an important resource.
They act as reservoir-type carriers and possess qualities which can make them ideal for certain posterior segment uses [66],[67].
