In 1818 he declined an appointment as justice of the Rhode Island Supreme Court, finding the appointment incompatible with his college office.
Beiser was widely regarded as an authority on the Rhode Island Supreme Court.
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He was reelected to the Seventy-third and Seventy-fourth Congresses and served from November 4, 1930, until his resignation on January 10, 1935, having been appointed an Associate Justice of the Rhode Island Supreme Court in which capacity he served until January 7, 1958, when he was appointed Chief Justice.
The Providence County Courthouse in College Hill, Providence, where the Rhode Island Superior Court, the Rhode Island Supreme Court, and the Rhode Island Law Library are located, and where Licht served as a Justice on the Rhode Island Superior Court, was named the Frank Licht Judicial Complex in 1986, in honor of the former Governor, and Justice of the court.