Holtslag studied recorder with Kees Boeke at the Sweelinck Conservatorium in Amsterdam (now Conservatorium van Amsterdam), graduating with distinction in 1980. He has toured worldwide as a recorder and flauto traverso player, performing with a number of distinguished musicians such as Gustav Leonhardt, William Christie and Roy Goodman as well as with ensembles such as The English Concert, Orchestra of the 18th Century, Akademie für Alte Musik Berlin, La Fontegara Amsterdam and Trio Noname. He has recorded numerous CDs for major labels, including Hyperion, DGG/Archiv and Chandos.
From 1984 to 1988 Holtslag taught at the Guildhall School of Music in London, in 1988 appointed a professor in the Royal Academy of Music in London and Hochschule für Musik und Theater Hamburg. From 2008 visiting professor in the Academy of Music in Kraków. Honorary Associate of the Royal Academy of Music.