As an independent sub-contractor are you required to get professional liability insurance?

This depends on a number of things. It's hard to say without knowing what kind of work you are sub-contracting.

First determine if you need Professional Liability coverage Or Commercial Liability Coverage. They are very different products.

Most General Contractors do require the subs to carry insurance. Otherwise the General Contractor will have to pay much more for insurance coverage that effectively covers his or her own activities as well as those of the sub-contractors.

If the General Contractor you are doing work for already has coverage for his subs under their insurance (usually not).

What is the nature of your agreement with the General Contractor.

Some Contractors insurance policies cover subs while others do not.