If they are on the same circuit (which you say is the case) and the old-style switch loop is wired correctly (which you have to check) then:
Disconnect white wire at the switch with a white wire connected to it. Find the join in the associated light fixture between black and white and disconnect it, capping the always-hot black feed there, it will be unused. Also disconnect the neutral associated with the incoming always-hot from the fixture, as it will also be unused. Maintain any onward connections that may feed other fixtures.
Run 14/2 (/3 is not useful) between the two switches, connected to always-hot and neutral (probably black to black and white to white and ignore red, but not a guarantee, just a convention to use red for switched hot.)
At the switch formerly without neutral, join your white neutral wire to the white, and your black always-hot to the switch. Be nice to your (future) self and put some red tape on the black wire going to the light connected to the other terminal on the switch.
At the associated light, connect the black coming from the switch to the fixture (which it already should be) and the white coming from the switch to the fixture white/neutral. DO NOT connect the white from the switch to the other neutral(s) in the light box. If the switch black is not connected to the light, you need to identify it and remove it from an improper switch loop connection to always-hot.
This is required to keep hot and neutral in the same cable. You can't just bring over neutral without also bringing that neutral to the associated light in the same cable as it gets hot. And you can't make loops unless you are on British-derived rules.