This hole, to in a stud wall needs to be filled. The best way to deal with this is cut out a square area around the hole. As the wall has a cavity there is nothing for any filler to stick to.
Once l have cut out and removed l fix some wooden battens behind, this will give a support for the new plaster board to fit into. Now a quick coat of plaster. Once the plaster is dry give a sanding to prep for painting, you won’t even know it was there.
Handyman services for the small jobs that others won’t do.