Old Light Switch Not Grounded

Does your new switch require a neutral? If so, is there one tucked into the back of the box?

Switches do not require a ground to work, although some can use the ground in place of a neutral. If there is a ground wire in the box then wire nut it to the ground wire of the switch.

Agree with @daveb1 .
Also, last guy made joint poorly. Uninsulated wire should not extend outside
of wire nut.

daveb1 said:

Does your new switch require a neutral? If so, is there one tucked into the back of the box?

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Although it is now code, it wasn't for decades.
It is not uncommon to find only a switch leg in a switch box.
You will be fortunate to find one if you home is older.