"encounter that" is correct and usable in written English.
You can use it when referring to a situation or experience. For example, "She had an unexpected encounter that changed her life."
It was the encounter that defined his campaign.
Ms. Paglia calls it "an encounter" that was "unsuccessful".
Her daughter Kate, 6, may never encounter that problem.
A cinematic encounter that turned into a history for history-less subjects.
Collins also recalled a personal encounter that helped inspire her life in politics.
It's exhilarating to encounter that kind of confidence and risk on the page.
And believe it or not, Tuesday had a third close encounter that finished 2-2.
They eventually found him at his family's home — an encounter that led to his death.
The mystic experiences God in an inexpressible encounter that is beyond mundane human experiences.
The encounter that aired on CBS was short — less than seven minutes.
"There are forms of experience and encounter that are absolutely of the moment".
