[2] Carter came under the mentorship of Richard Gill, one of Australia's leading music educators and conductors,[3] and conducted his first opera production, Hans Krása's Brundibar for OzOpera in 2004.

[2] Young appointed Carter as Kapellmeister and musical assistant at Hamburg State Opera from 2011,[5] which saw him conduct The Magic Flute, Hänsel und Gretel, Lucia di Lammermoor, The Barber of Seville as well as assisting Young on a broad repertoire that including all ten Wagner operas.

[6] From 2014, Carter was appointed Kapellmeister at the Deutsche Oper Berlin, working closely with Sir Donald Runnicles.

His repertoire expanded, conducting productions of The Love for Three Oranges, La bohème, Prokofiev's Romeo and Juliet, L'elisir d'amore and Die Entführung aus dem Serail.

[10] In November 2024, Staatsoper Stuttgart announced the appointment of Carter as its next General Music Director, effective with the 2026–2027 season.