Encontrei “Vara Mista” traduzida para PT-Br como “Mixed Court” (veja exemplos abaixo.) Quanto a “comarca”, o dicionário do Marcílio recomenda traduzir tal termo como “judicial district”.

“… serão examinadas sentenças oriundas da 6a Vara Mista da Comarca de Sousa/PB.”
“… we will examine sentences from the 6th Mixed Court of Sousa/PB District Court.”
http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/16233...

Example Sentences

“For cases o f serious crime a number o f European countries employ a variant oJthe jury called the mixed court, in which laymen and professional judges sit together in a single panel that deliberates and decides on all issues of verdict and sentence.“ https://law.yale.edu/sites/default/files/documents/pdf/Facul...

“Although they had analogues in the Ottoman Empire and elsewhere, mixed courts achieved their classic form in Egypt between 1875 and 1949.“
https://www.encyclopedia.com/humanities/encyclopedias-almana...