Indeed "Labor Court" would work; however, for "juzgados laborales" you might check if those are labor trial courts to distinguish from the national appellate labor court within the labor court system. Really depends on which country/legal system your document deals with, though.



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Note added at 36 mins (2019-08-23 05:10:15 GMT)
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In Spain it goes like this:

Órganos de la jurisdicción social/labor (or: Órganos jurisidiccionales del orden social/labor) --> Labor courts
Juzgados de los Social --> Labor Trial Courts

Sala de lo Social de los Tribunales Superiores de Justicia de las Comunidades Autónomas --> Labor Division of the Superior Courts of Justice of the Autonomous Communities
Sala de lo Social de la Audiencia Nacional --> Labor Division of the National Court
Sala Cuarta de lo Social, del Tribunal Supremo --> Labor Division of the Supreme Court

Source: Rebecca Jower (Thematic Lexicon of Spanish-English Legal Terminology)