After his father's death, his mother married the director of the Danish Asiatic Company, Peter van Hurk (c.

[2] In 1760, Abbestée returned to Tranquebar and upon H. J. Forch's death, on 29 April 1761, was elected as the colony's acting governor.

He represented the company in the commission which was set up in connection with the transfer of the East Asiatic colonies to the state in 1777.

He and his family boarded the ship Dronning Juliana Maria in December, bound for Tranquebar, but the voyage ran into complications and did not arrive until 16 January 1779.

It was granted him but due to deaths among his colleagues, he ended up acting as governor until finally being replaced by Peter Anker in 1788.

[4] Alongside his office as governor, Abbestée also worked as a trader, partly backed by Anglo-Indian capital.