The former Denmark U21 goalkeeper started his career with FC Nordsjaelland, making his debut in August 2011 against Hillerod Fodbold.
Spells followed on loan at FC Frederica and AB before his breakthrough campaign came at Nordsjaelland in 2013/14, where he made 16 league appearances.
David then became first-choice keeper for two seasons before moving to Dutch Eredivisie side Utrecht in July 2016.
He made his debut against Feyenoord and in his first season helped the club to fourth place in the division and qualification for the Europa League.
A regular for three seasons, he joined New York Red Bulls in January 2020 and made his debut in a 3-2 win over FC Cincinnati on the opening day of the MLS season.
He has represented Denmark from U16 to U21 levels.