Upon his graduation he studied clarinet with Keith Wilson and composition with Mel Powell at Yale University, where he received a Master of Music in 1963.
In the meantime he performed as a clarinetist in the Netherlands Wind Ensemble and the Connecticut Symphony Orchestra.
In 1965 he accepted an appointment for professor of clarinet and composition at Brandon University in Manitoba, which he held until 1971.
He then taught at the music conservatories of Enschede, Arnhem, and Groningen until 1990.
Hekster was married from 1962 to the US-born and Yale-educated bassoon player Alice Hekster-van Leuvan.