Zámbó came from a minor Transdanubian noble family and began his career as a squire of the queen dowager of Hungary, becoming a chamber count and castellan of Óbuda. He was one of the men used by the queen, Elizabeth of Bosnia, and Palatine Nicholas I Garay to form a new, reforming government. Beginning in 1377, Zámbó was in charge of the kingdom's finances, holding the office of archtreasurer, and was appointed treasurer (Latin: magister tavarnicorum) in 1382, the same year Elizabeth's daughter Mary succeeded to the Hungarian throne.
Zámbó also held the office of Jew judge (Latin: judex Judeorum), and as such, his primary task was to deal with litigations between Christians and Jews. He took advantage of the turmoil that followed Queen Mary's accession and attempted to gain fortune for himself at the expense of Jews he was supposed to protect. He had several of them arrested and maltreated, confiscating their property. Upon her return from Croatia-Dalmatia, Elizabeth exempted the Jews of Buda, Pressburg, Sopron, Nagyszombat, Székesfehérvár, and other cities from Zámbó's overlordship until he agreed to pay them out for the injuries inflicted upon them.
In August 1384, Zámbó, along with Nicholas Szécsi and the House of Lacković, renounced allegiance to Queen Elizabeth, who ruled in her daughter's name as regent, due to her intention to break Mary's engagement to Sigismund of Luxembourg and have her married to Louis of France.
- Engel, Ayton, Pálosfalvi, 189.
- Patai, 62.
- Engel, Ayton, Pálosfalvi, 196.
- Patai, Raphael (1996). The Jews of Hungary: history, culture, psychology. Wayne State University Press. ISBN 0-8143-2561-0.
- Engel, Pal; Ayton, Andrew; Pálosfalvi, Tamás (1999). The realm of St. Stephen: a history of medieval Hungary, 895–1526 Volume 19 of International Library of Historical Studies. Penn State Press. ISBN 0-271-01758-9.