At graduation, he featured in the title role of William Shakespeare's play Henry V, presented as a Royal Command Performance for King George VI and Queen Elizabeth.

He later performed on Canadian Broadcasting Corporation radio beginning in 1951 and continuing to the 1980s, including the long-running series A Touch of Greasepaint, the Joe McCarthy–inspired The Investigator, and 1984.

The hour-long special audio drama comprised a half-dozen vignettes and performances culled from theatrical history, including Shakespeare and Shaw.

Morse made his movie debut in the 1942 comedy The Goose Steps Out featuring Will Hay and continued with roles in Thunder Rock, When We Are Married, and This Man Is Mine (released as A Soldier for Christmas in North America) with Glynis Johns and Nova Pilbeam.

He also appeared in the thrillers Asylum (1972) with Peter Cushing, Funeral Home with Kay Hawtrey and Lesleh Donaldson (1980), and The Changeling with George C. Scott (1980).

Morse performed on Broadway in Hide and Seek, Salad Days, and the lead of Frederick Rolfe in Hadrian the Seventh, which he also played in Australia, co-featuring with Frank Thring.

He directed the Broadway debut of Staircase featuring Eli Wallach and Milo O'Shea, a depiction of gay male life.

With his son Hayward Morse, he featured in the 2004 North American debut of Bernard and Bosie: A Most Unlikely Friendship by Anthony Wynn, performed at the University of Florida, Sarasota.

The next year, Morse appeared in the world premiere performance of the science-fiction play Contact by Doug Grissom, co-featuring Ryan Case and presented in Tampa, Florida.

Some of his best-known television roles included: Lt Philip Gerard for the 1960s series The Fugitive with David Janssen; Victor Bergman in the 1975–76 season of Space: 1999 with Martin Landau, Barbara Bain, and Zienia Merton; Mr Parminter in The Adventurer with Gene Barry; and Alec "the Tiger" Marlowe in The Zoo Gang with Sir John Mills, Lilli Palmer, and Brian Keith.

In 1982, he played the Reaganesque U.S. President Johnny Cyclops in the satirical sitcom Whoops Apocalypse in the UK and hosted the series Strange But True for the Global and the BBC.

It featured a colour photo section of models created for the Space: 1999 television series by Martin Bower, and a foreword by Zienia Merton.

Before his death, Morse wrote the foreword to Conversations At Warp Speed (ISBN 9781593932893), published in 2012 by BearManor Media, and written by Anthony Wynn.

[4] His body was donated to science, and on 3 April 2011 Morse's ashes were scattered in St. James's Square Garden, Pall Mall, London, England.