If the other switch is a plain old dumb switch, it does not need a neutral although it is possible that one of the wires going to its predecessor is white. Although the most modern code (set forth in the latest NEC book) requires neutrals in switch boxes, replacing a plain dumb switch with a decorative dumb switch is a grandfathered maneuver that does not require restringing cables to have a neutral.
With rare exceptions dumb switches do not have neutral terminals. Most switches do have ground terminals, usually a green screw on the frame (yoke; mounting strip).
I have seen a very old dumb switch that has, in additon to the usual pair of regular terminals, two neutral terminals that have nothing between them except an internal straight bar to pass through the neutral path in lieu of wire nutting the neutral wires in the box.
If you pigtail* the neutral for this new smart or dimmer switch from another cable feeding a different switch or device then you must pigtail the raw hot from that same cable to power the new switch and applicable light.
* If one wire end wants to be connected to two things then cut two short lengths (pigtails) and wire nut those to the wire end in question. Now you have separate wire ends to connect to the two things.
With rare exceptions dumb switches do not have neutral terminals. Most switches do have ground terminals, usually a green screw on the frame (yoke; mounting strip).
I have seen a very old dumb switch that has, in additon to the usual pair of regular terminals, two neutral terminals that have nothing between them except an internal straight bar to pass through the neutral path in lieu of wire nutting the neutral wires in the box.
If you pigtail* the neutral for this new smart or dimmer switch from another cable feeding a different switch or device then you must pigtail the raw hot from that same cable to power the new switch and applicable light.
* If one wire end wants to be connected to two things then cut two short lengths (pigtails) and wire nut those to the wire end in question. Now you have separate wire ends to connect to the two things.