Gibbs' editing career began in the mid-1950s as an assistant to Ralph Kemplen and to Alan Osbiston, and through them he became involved with the brief "New Wave" of British filmmaking at its beginnings.

Gibbs was then principal editor for several of the subsequent "New Wave" films, including Richardson's A Taste of Honey (1961), The Loneliness of the Long Distance Runner (1962), and Tom Jones (1963),[4] and also The Knack ...and How to Get It (1965), which was directed by Richard Lester.

In his 1995 book, Film and Video Editing, Roger Crittenden notes the influence of this first phase of Gibbs' editing career, "The generation of American editors of which Dede Allen is a part has given considerable credit for the inspiration of their work to Antony Gibbs, the English editor of films directed by, amongst others, Tony Richardson, Nicolas Roeg, and Richard Lester.

There is a daring and energetic quality to Tony Gibbs' work, especially in some sequences of The Loneliness of the Long Distance Runner, Tom Jones, The Knack, and Performance, which must have given a shot of adrenaline to aspiring editors on both sides of the Atlantic at the time.

"[5][6] Bonnie and Clyde (1967) "marked a turning point in the editing of feature films that sent reverberations through the entire American cinema.