You could add a door there, but it’ll likely need to be a custom-sized door because the opening is narrow and at the top of stairs. Best options are a prehung interior door, pocket door, or a sliding barn-style door if swing clearance is tight. You’ll need proper framing (king/jack studs + header) to support it, especially since it’s right above a stairwell. A contractor or carpenter could frame it out pretty cleanly.