Gorter was born in Amsterdam on 30 May 2000 and signed a four-year contract with Ajax in the summer of 2021. Before that, the goalkeeper had been part of the Go Ahead Eagles selection for three seasons. He gained entry into the Eredivisie in 2021 with the club from Deventer.
The goalie made his Ajax first team debut on 20 January 2022 in the cup-winning match against Excelsior Maassluis (9-0). So far, he played three official matches in the first team. Previously, Gorter played in Ajax's youth team between 2010 and 2014.