Eastern Province noun6 •A province of Saudi Arabia. Capital: Dammam."I was shocked to see girls this young wearing the cloak," says the author, who encountered this group of schoolgirls near Qatif oasis in the Eastern Province. — 1987 •A province of Sri Lanka. Capital: Trincomalee. •A province of Zambia. Capital: Chipata. •A former province of Kenya. Capital: Embu •A province of Sierra Leone. Capital: Kenema. •A province of Rwanda. Capital: Rwamagana