you add a new switch. two ways to handle it, have new switch installed for the fan that controls both the fan speed and the light in one switch and then add a second for recessed. or have three wall switches.

Or wire the fan to be on all the time and use a remote (many fans come with them and they area available as retrofits).

I assume you have a two-gang electrical box (example). Swap the light and fan switches for one double-switch (example). Run a new cable from the electrical box to dimmable recessed lights. Install a dimmer (example) in the electrical box to control those lights. Why not just wire the new recessed lights to the fan? In my experience LED recessed lights can be extremely bright and you want to be able to reduce the brightness with a dimmer.

Thank you everyone! I was able to do it! Wiring the box was the most difficult part, but everything went well