Carter was born in the London parish of Shoreditch, and while still young gained the silver medal of the Society of Arts for drawing.
He was first articled to Edmund Turrell, an architectural engraver, but later concentrated on landscapes and figures.
[1] When the engravings from the Vernon Gallery appeared in The Art Journal, Carter was given The Village Festival, painted by Frederick Goodall.
It was followed in the same series by engravings from The Angler's Nook, painted by Patrick Nasmyth, and Hadrian's Villa, painted by Richard Wilson; Edward Matthew Ward then asked that Carter should engrave his picture The South Sea Bubble, and subsequently employed him to engrave Benjamin West's First Essay in Art, a large plate he completed a short time before his death.
[2] Other works by Carter were a plate from his own design of Cromwell dictating to Milton the Despatch on behalf of the Waldenses, and a portrait of Sir Marc Isambard Brunel, after Samuel Drummond.