Much more info is required. First, is there an unfloored attic above the kitchen? That would (usually) make it easy. If not, there are many different possibilities that could affect the ease or difficulty of this job - such as which way to the joists run in the ceiling above the kitchen? You should probably get some technical assistance.

More info is needed, as rlpxqrstuvlmnxyz noted. I doubt there is an exposed attic above the light because you probably would not have asked, otherwise.

The direction of joists in the ceiling will determine if it is difficult or not. If it is along the same direction as the joists, you can just feed wire through the gap, and it will not be that difficult. If, however, you are trying to cross the joists, you will need to cut into the ceiling in a few spots to drill holes and feed the wire through them. You need not cut a "trench" but you will need to cut access holes in the ceiling drywall so as to drill through the joists. Patching the ceiling will be a bother.

You will also need to keep the existing box as a junction box so that the splice between the existing wire and the extension wire is inside a junction box. Cover it with a flat plate. DO NOT REMOVE THE ORIGINAL BOX unless you re-wire the entire circuit such that there are no wire nut connections between two wires. (I doubt you will re-wire; if you knew that much, you would not need to ask the question.) It is very dangerous to leave exposed wire nut connections outside of a junction box.

Supporting the new light fixture will be the next task. The easiest solution would be to find the joist, cut the access hole for the new junction box right next to the joist, and secure the new junction box to the joist. Alternatively, there are retrofit ceiling light fixture boxes that you can use. A ceiling light will require more support than a simple recessed light fixture.