You have two conflicting answers. I think I agree with Tom. However, it may be impossible to tell if it's correct without more context. Maybe you could post the entire sentence.

Absolutely. "A great danger" is a noun. It is grammatically correct to put ANY preposition in front of it: about a great danger before a great danger near a great danger following a great danger over a great danger at a great danger behind a great danger, ... and so forth. There are over a hundred possibilities. Some will be more useful than others but none is wrong. If you give me just about any a preposition, I can make a sentence in which that preposition makes sense with "a great danger". For example: "On their hike, Alice an Mary arrived at a swamp teeming with alligators. They became fearful as they sensed they had arrived at a great danger."

No. At great danger.