Investement advisor and securities brokerage firms are required to be locally incorporated in Zambia. Branches of foreign companies are not allowed.
SCHEDULE (Rules 4-7)
PART I-  STRUCTURE AND OPERATION OF A COLLECTIVE INVESTMENT SCHEME
SECTION A-ROLE OF THE TRUSTEE/CUSTODIAN
2. A trustee/custodian shall be- Qualifications for appointment
(a) a bank registered under the Banking Act, or licensed or registered under any Act amending or replacing that Act; or (b) a trust company which is a subsidiary of such a bank; or (c) a trust company registered under the Companies Act; or (d) a banking institution or trust company incorporated outside Zambia, which has a subsidiary incorporated in Zambia, and which is acceptable to the Commission.
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SECTION B-ROLE OF THE MANAGEMENT COMPANY AND AUDITOR
7. Every collective investment scheme for which authorisation is requested shall appoint a management company acceptable to the Commission, except as provided for self-managed schemes below.
8. A management company shall- Requirements for management company
(a) be engaged primarily in the business of fund management; (b) have sufficient financial resources at its disposal to enable it to conduct its business effectively and meet its liabilities; in particular, it shall have a minimum issued and paid-up capital and capital reserves of
ten million kwacha or its equivalent in foreign currency; (c) not lend to a material extent; and (d) maintain at all times a positive net asset position.
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12. (1) The type of licence required depends on the functions performed by the management company in Zambia. 
(2) Except as provided by subclause (3), a management company that is incorporated in Zambia shall be licensed as an investment adviser under the Act.
(3) However, should it undertake the distribution function in Zambia or otherwise deal in securities, it shall be licensed as a dealer.[...]" (Securities (Collective Investment Schemes) Rules, S. I 1631 of 1993)

Securities (Collective Investment Schemes) Rules, S. I 1631 of 1993
[<a href="http://www.seczambia.org.zm/wp-content/uploads/2017/06/THE-SECURITIES-COLLECTIVE-INVESTMENT-SCHEMES-RULES.pdf">Rule</a>]