His mother, Gitta, physically disabled from birth, encouraged him to pursue a career in shipping when he left school at the age of 15.
Joining A. P. Møller - Mærsk as an apprentice in Copenhagen, Denmark, Gullestrup was later transferred to London, United Kingdom in the late 1970s.
Gullestrup is accredited with helping drive Clipper Group to become the world's largest shipping company within a number of bulk segments and project vessels.
[7] A documentary was produced on the story,[8] and subsequently the Danish film, A Hijacking, based on the incident and loosely around Gullestrup's role in it.
As a direct result of the incident involving the Somali pirates, Gullestrup and other industry leaders started the Danish-Somali charity initiative called Fair Fishing in Somaliland.