In addition your light fixture may require mounting to a ceiling joist or to two short blocks nailed.
Run wire above ceiling joist no attic.
If there is access above the light in an attic or kneewall space you can remove the wire from the existing fixture box and install it in a junction box.
If you drill holes in the joists and run wire through those holes you ll be disturbing the insulation.
Worst can you open the ceiling 5 inches from the wall and work from there.
If the wires are within 7 of the attic access hole or along any attic flooring you ll need.
For vertical work you can cut about 6 inches below the wall ceiling joint drill through the top plat and then fish from the opening ion the ceiling.
You can then splice on a new piece of wire make sure it is the same wire gauge and run the new piece from the junction box back to the fixture box.
In some cases you can run the electric wire beneath the ceiling joists.
The actual install of recessed lights here https youtu be 5yc8aqnvqqg the long bit is actually used.
Running electrical wire through the channel between ceiling joists is generally easiest.
If there is any attic space at all or you get lucky with the joist bays you will likely be able to fish a.