Gamst was born on 3 September 1788 in Copenhagen, the son of Hans Christensen Gamst (1737–1803) and Marthe Marie Storch (1751–1830).
The company was continued by Gamst's mother and paternal uncle Johannes Christian Gamst (1751–1829) after the father's death in 1803.
[1] Gamst joined the family business as a partner in 1811 and became its sole owner in 1829.
In 1836 the name of the company was changed to H. Gamst & H. C. Lund when Gamst's nephew Hans Christian Lund became a partner.
[2] Upon selling his company in 1854, Gamst purchased Vedbygård at Holbæk.