You don't really want to run a power cable from a socket through the wall. You can but it's a massive bodge. You shouldn't need to use conduit inside the wall.
A lot depends on where your current socket is. If you've got lucky and it's directly under the back of the tv then you can run a spur to a socket behind the TV. You can only fit a new socket horizontally or vertically in line with an existing one. If you can go that route you may as well have the signal cables wired properly too, the ends of the cables make it difficult to find grommets or any neat finishing otherwise.
If you must run the standard cables through the wall you could still use a back box/front plate to try and neaten up the hole/save on making good. The cables should have a bit of mechanical protection if you think they will be dragging across metal etc, plastic is ok though.
You don't really want to run a power cable from a socket through the wall. You can but it's a massive bodge. You shouldn't need to use conduit inside the wall.
A lot depends on where your current socket is. If you've got lucky and it's directly under the back of the tv then you can run a spur to a socket behind the TV. You can only fit a new socket horizontally or vertically in line with an existing one. If you can go that route you may as well have the signal cables wired properly too, the ends of the cables make it difficult to find grommets or any neat finishing otherwise.
If you must run the standard cables through the wall you could still use a back box/front plate to try and neaten up the hole/save on making good. The cables should have a bit of mechanical protection if you think they will be dragging across metal etc, plastic is ok though.