Complex sentence: Temporarily shelving hopes for promotion he accepted the Sir John Orde, the Governor of Dominica's, request took command of the government brig "Lord Howe" and carried out anti-smuggling operations until July 1789.
Split into simpler sentences: Temporarily shelving hopes for promotion, he took command of the government brig "Lord Howe" at the request of Sir John Orde, the Governor of Dominica. As captain of the "Lord Howe" he carried out anti-smuggling operations until July 1789.