Does my client contract set my insurance requirements?

Often it does. Professional services agreements commonly specify limits, additional insured or certificate requirements, notice periods, and sometimes the type of form. The contract controls on its own terms, which means the answer is in the document rather than in a general standard for your industry. One request to watch for is adding your client as an additional insured on the professional liability policy. That is generally not available on this line, and it can work against them, because once they are an insured an insured-versus-insured exclusion may bar the claim they wanted to preserve. A waiver of subrogation is a different request and can often be endorsed on. Read the insurance article of the agreement before you sign it, and where an indemnity or limitation of liability clause is involved, review it with counsel.