There are no dimensions, so only going by graphic representation and so what looks like a large 9' pool table.

It seems that the impetus for this project, seeing the relocation of the existing bar, is to allow the new pool table to fit. And noting there is only a tv by the pool table. It is very tight around the table, so you may be maneuvering both the table, the furniture, and tv for better placement as time goes on with use. You may even tire and get rid of the table if playing on it is too difficult because of the contortions required for unencumbered play. I say this thinking that you may need flexibility in the lighting layout. So I would stick with a general grid of lights over the entire space. Divide the space into 2 sections - seating and pool table area - on different switches. So (3) switches: seating recessed, pool table recessed, and center hanging fixture for the pool table.

Not considering accent lighting on any walls or at the new wall counter bar, that is probably obvious on how to provide lighting.

Thanks @3onthetree. The den is approximately 12' x 20'