Maister was baptized on 1 February 1699, the eldest son of William Maister, a merchant of Hull. In 1716, he succeeded his father, and ran the family mercantile business with his brother Nathaniel. He married Mary Tymperon, daughter of Rev. Henry Tymperon of Carnaby, Yorkshire on 25 August 1724. She died in of smallpox in 1725. He married as his second wife Mary Cayley, daughter of Sir Arthur Cayley, 3rd Baronet, of Brompton, Yorkshire on 19 January 1727 
Maister was Sheriff of Kingston upon Hull in 1729. He was returned unopposed as Member of Parliament for Kingston upon Hull at a by-election on 6 February 1734, and then elected in a contest at the 1734 British general election soon after. He voted regularly with the Government. He did not stand in 1741.
Maister and his wife several children. On 13 April 1743 a fire destroyed the family house in High Street, Hull and his wife Mary and her infant son died, along with two maidservants. The family deeds, plate and portraits were destroyed in the fire. Maister immediately began rebuilding on the same High Street site  He died on 15 December 1744.
- Hullweb History of Hull The Maister Family
- "MAISTER, Henry (1699-1744), of Hull and Winestead, Yorks". History of Parliament Online. Retrieved 31 March 2019.
- National Trust, Maister House
|Parliament of Great Britain|
| Member of Parliament for Kingston upon Hull
With: George Crowle