We have a trust office within our banking company. The trust office is located in a different office than our bank and branches. Does the trust department have to provide Initial or Annual Privacy Policy notices under Reg P?

In general, regulation P (and its parallel regulations) apply to every department of the bank; there is no exclusion for the Trust Department. The issue is whether the customer is a consumer. Some of your customers are companies, some are entities (trusts & estates) and some are simply consumers. You must make the same distinctions that the rest of the bank does in determining whether the initial and annual notices are required.