He gained a First Class degree in Moderations in 1852, a First in Literae humaniores in 1853 and a First in School of Law and Modern History in 1854.
[1] He was called to the bar by Lincoln's Inn, where he practised as a conveyancer and equity barrister.
[1] He was a leader writer for The Times under John Thadeus Delane and in 1870 he succeeded George Webbe Dasent as the paper's assistant editor.
When Delane retired in 1877, Stebbing edited the paper until Thomas Chenery was appointed in 1878, whereupon Stebbing retired as assistant editor, although he still contributed articles.
In 1870 he married Anne Pinckard Pidgeon (the daughter of Jonathon Sills Pidgeon) with whom he had three sons and two daughters.