A Zambian company can sell into another African market before it needs a local subsidiary there.
Growth beyond Zambia does not automatically require another company.
The operating requirement comes first
The appropriate entity should follow the commercial and operational requirements of the expansion, rather than being selected first.
Depending on the market and activity, direct contracting, a distributor or agent, a subsidiary or a joint venture may be relevant. The appropriate model depends on the commercial and regulatory circumstances.
A local entity may become justified where substantial people, regulated activity, procurement, delivery, customer obligations or investment require it. In other circumstances the Zambian company may continue to serve the market effectively.
Additional entities must earn their cost
A cheap entity with no bank, people, licence or purpose is expensive.
A new market may introduce company-law, tax, employment, investment, sector, banking or competition consequences. Appropriately qualified specialists in the countries involved must confirm which of those consequences apply.
A subsidiary is justified when it makes the business more capable, governable and legible. If it only changes the address on the invoice, the real work is still unfinished.