Several years later, following his service with the U. S. Marines in World War I, rather than return directly to the United States, Connolly went to Ireland, where he enrolled in a number of non-theatre-related courses at the University of Dublin, reportedly with the intention of abandoning the profession altogether.

[1] Within four months of his return to the States,[2] Connolly was being praised for his work alongside Margaret Anglin and others in Paul Kester's adaptation of Henry Kistemaeckers' play, The Woman of Bronze.

[3][4] Between the years of 1916 and 1935, Connolly was a successful stage actor who appeared in twenty-two Broadway productions, notably revivals of Pirandello's Six Characters in Search of an Author and Chekhov's Uncle Vanya.

His trademark role was that of the exasperated business tycoon or newspaperman, often as the father of the female lead character, as in It Happened One Night (1934) with Clark Gable and Claudette Colbert; Broadway Bill (1934), supporting Warner Baxter and Myrna Loy; and Libeled Lady (1936) with William Powell and Loy again.

Connolly mostly played supporting roles, but starred occasionally, as Nero Wolfe in The League of Frightened Men (1937), in RKO's 5th Ave Girl (1939), opposite Ginger Rogers, and as the title character in The Great Victor Herbert (1939), his last film.