What happens when a charged insulator is placed near an uncharged metallic object?

So when the charged insulator is placed near the uncharged metallic thing they both attract each other because there will be a distribution of charge between the insulator and uncharged object. This migration of charges happens regardless of their charge positive or negative.

They attract each other.

When the charged insulator (regardless of whether + or - ) is brought near an uncharged metallic object, electrons will migrate on the metallic object so that the area near the charged insulator is the opposite charge (and, by conservation of charge, the area of the conducting object away from the insulator will have an excess of the same charge as the insulator).

Because opposite charges attract and the opposite charge on the conducting object is closer, the dominant force will be one of attraction.

If they are allowed to touch, the conducting object will then have the same charge as the insulator and the objects will repel.