Squire made her Broadway stage debut in 1927 in
Much Ado About Nothing. She later appeared in Broadway productions of
Goodbye Again (1932), ''Hipper's Holiday
, Three Men on a Horse (1937), and Lady of Letters'' (1935), among other plays. In 1951, Squire made her television debut in an episode of
Pulitzer Prize Playhouse. For the remainder of the decade, she appeared in guest roles on
Goodyear Playhouse,
Robert Montgomery Presents,
Westinghouse Studio One,
The United States Steel Hour, and
Playhouse 90. In 1954, she portrayed Gertrude Harper in the CBS drama
Woman with a Past. From 1956 to 1957, Squire had a recurring role in the soap opera
Valiant Lady. She made her feature film debut in the 1959 drama
The Story on Page One. Squire also continued acting on the stage with roles in
The Traveling Lady,
Six Characters in Search of an Author,
The Sin of Pat Muldoon, and
The Shadow of a Gunman. During the 1960s, Squire continued her career in films, television and stage roles. In 1960, she made two guest appearances on
Alfred Hitchcock Presents, and appeared as the mother of
Dirk Bogarde's character in
Song Without End. Squire returned to the stage the following year in a co-starring role in the New York production of
Roots, by
Arnold Wesker. On television, she portrayed the title character's mother in
Dr. Kildare. From 1962 to 1963, she guest starred on two episodes of
The Twilight Zone: "
One More Pallbearer" and "
In His Image". She made three guest appearances on
Perry Mason: Clara Thorpe in the 1960 episode "The Case of the Credulous Quarry," Vera Hargrave, the murderess, in the 1964 episode "The Case of the Nervous Neighbor," and Esther Norden in the 1965 episode "The Case of the Wrongful Writ." She had additional guest roles on
The Road West,
Peyton Place, and
Adam-12. In 1971, Squire co-starred in the
road film Two-Lane Blacktop. Starting in 1970, she had a recurring role in the long-running soap opera
The Doctors. In 1974 and 1975, Squire had her third recurring role on the soap opera
Search for Tomorrow. Her last television appearance was in 1975 in the
Hallmark Hall of Fame television film
Eric, as Mrs. Harris. For the remainder of her career, Squire appeared in roles in regional theater. In 1979, she had a leading role in
Hillbilly Women at the Long Wharf Theater in New Haven, Connecticut. In the early 1980s, she acted in
Hedda Gabler (starring
Susannah York) at the Roundabout Theater, and in
Memory of Whiteness at the American Place Theater, both in New York. Squire's final onscreen role was in the romantic comedy film
When Harry Met Sally... in 1989. ==Personal life==