private company
US /ˈpraɪ.vət ˈkʌm.pə.ni/
UK /ˈpraɪ.vət ˈkʌm.pə.ni/

1.
a company whose shares are not traded on a stock exchange and are held by a small number of shareholders, often family members or a small group of investors
:
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He decided to keep his business a private company rather than going public.
•
Many small businesses start as private companies.