If a neutral metal comb is held near an object with a negative charge, the Como become charged by

induction

contact

friction

static discharge

The local charging of the comb is due to induction. The negative object's charge pushes electrons in the comb away from the side close to the charged object causing that part to be positively charged. Note that the comb's net charge is still zero provided it doesn't touch the object. When you move the comb away its electrons will redistribute.