Any thoughts on what the optimal spacing between fixtures is for a recessed lighting layout? I'm replacing a fluorescent light box setup with recessed in an 11 ft. by 21 foot room.

Hi, I recently purchased a home and in the living room was a older type of light fixture. We want to add a new light fixture there but I am at a loss in how to best do this job. When I take the light off there is a light box in the ceiling and I'm not sure if I have to pull the whole box out and then patch the plaster ceiling or how to best do it. I hope this makes sense since the box is really big compared to the small round base of the new light that we want. Ill include pictures of the living room where you can see the old light fixture and Ill also add the newer kind that we want. Any help would be highly appreciated. Thank you in advance. (Please excuse the mess around the house.)