You can’t fix the video. It’s overexposed. There is nothing to recover. You can use a curve and pull down only the high whites (the upper right corner of the curve). You will have to put a second point on the curve to prevent dimming the mid range and low tones. That would make it grayer and less obvious.
You could replace the blown out pupil with, for example, a photoshop image, but that would require a LOT of keyframing to keep the still image in the right place on the video.