I did this in our house recently, not above the fireplace though 🙂
Walls are breeze block with a gap between that and the plasterboard so as above hole top and bottom and drop the cables down then use those AV plates with brushes on to cover the hole. I dropped 3 hdmi cables, 2 network cables (one for the powerplug going into a hub and the other for the tv, optical cable, a standard aerial cable in case I ditch sky and switch to freeview, and a length of string.
Oh and just to explain waht the cables were for – hdmi – sky/apple tv/games console, network cables – powerplug plugged into double socket spur behind tv, one cable going to network hub, one coming from hub to tv, optical cable for a sounbar, string in case I need to run another cable (tie it to the cable and pull).
What are you doing about power for the tv? It’s not good practice to drop the power cable down the wall. If you’re comfortable with electrics then run a spur from a nearby socket.
What are your walls made of?