HAVANA — His business was among the first registered in Cuba in 2021 when the communist-run country began allowing private enterprise, banned since 1968.

Now, as the government tightens its grip over the private sector, Gabriel Mosquera Mourlot, 24, fears he may lose the wholesale business he runs, importing items such as pasta, rice, chicken and appliances in a country known for chronic shortages. He then sells them to businesses in the eastern province of Santiago and in the capital,…