Complex sentence: In Perugia the "magistratura dei Priori", "magistrature of the first citizens", was established in 1303: the palazzo had been called the "Palazzo Nuovo del Popolo" ("New Palace of the People") to that point.
Split into simpler sentences: In Perugia the "magistratura dei Priori", "magistrature of the first citizens", was established in 1303. The "Magistratura dei Priori" was housed in the structure, which had been called the "Palazzo Nuovo del Popolo" to that point.