Carmel worked on Broadway from the late 1950s into the mid-1960s. He played multiple parts in
The Power and the Glory (1958). He originated the roles of the 3rd Poet in
Caligula (1960), Pasha in
Once There Was a Russian (1961), The Deputy in
Purlie Victorious (1961), and Mr. Andrikos in
The Irregular Verb to Love (1963). He replaced Jack Creley in the role of Cardinal Wolsey in
A Man for All Seasons (in 1962) and also replaced James Grout in
Half a Sixpence (in 1966). On television Carmel starred as the henpecked husband Roger Buell in the 1967 first season of the NBC sitcom
The Mothers-in-Law, but was replaced by
Richard Deacon in season two. When the first season ended, creator and producer
Desi Arnaz told the entire cast that the show had a five-year guarantee but there was no money to give the contractual raises for the second season. While the other cast members agreed to forgo their salary increases, Carmel refused to forgo his. Carmel believed that Arnaz was illegally taking four salaries from the series—producer, creator, writer, and director—and this led him to quit the show (the series was canceled the following year). Carmel's television guest roles included the accountant Doug Wesley on
CBS's
The Dick Van Dyke Show and Colonel Gumm on
ABC's
Batman. He played the flamboyant and hapless galactic criminal
Harcourt Fenton "Harry" Mudd in two episodes of the original series of
Star Trek, "
Mudd's Women" (1966) and "
I, Mudd" (1967), and one episode of
Star Trek: The Animated Series, "
Mudd's Passion" (1973). He also appeared in roles on
The Patty Duke Show;
I Spy;
Blue Light;
The Everglades; ''
Hogan's Heroes; Car 54, Where Are You?; Banacek; The Man from U.N.C.L.E.; The Munsters; Voyage to the Bottom of the Sea; Hawaii Five-O; The High Chaparral; McMillan & Wife; All in the Family, and The San Pedro Beach Bums. He was a regular contestant on Pantomime Quiz, also known as Stump the Stars
. His film roles included Gambit, Myra Breckinridge, Breezy, Thunder and Lightning'', and
Jerry Lewis's comeback film
Hardly Working (1981). ==Later life and death==