Zvi was born on November 23, 1927, in Tel Aviv to Hayim and Haya Frank. The house was religious, and Tzvi received his formal education in Bilu Religious School and Gymnasium Moriah, through tenth grade. At age twelve, he joined HaEda, the religious Scouts; at age fourteen, he joined Beitar, then IZL; in 1943, he moved on to Lehi.
After abandoning his studies, he devoted himself to Lehi full-time, receiving a monthly stipend for rent and food.
In Jerusalem, his positions included: supervisor of the youth cells; supervisor of Dept. 6; recruiter and contact for supporters. Tzvi took part in all the operations: putting up posters, disseminating underground materials, surveillance and observation ahead of operations, mining roads at the entrance to the city, attacking the CID in the Russian Compound, and the attempted jailbreak at the Jerusalem Central Prison.
He also met Ruthie (Yona Zuckerman), a fellow freedom fighter, and in 1950, they married.
After the Partition Plan, Tzvi was transferred to Samaria and the south, where he was the supervisor of the youth cells, until he enlisted in the IDF.
With the establishment of the State, he was one of the Lehi members who received an exemption so that he could continue his political and educational activities. However, once he reached the conclusion that Lehi had served its purpose, he enlisted in the IDF, on September 2,1948. He served 27 years in the Artillery Corps and Armored Corps: two in mandatory service, then re-upping for eighteen years, then seven more years as a reservist. Tzvi was part of every war and ongoing security operation, all along the borders of the country, until after the Yom Kippur War. He was discharged from his permanent service as a lieutenant colonel, commander of an artillery battalion. He was a graduate of an armored commanders’ course and the Command and Staff College.
With his completion of his permanent service in 1968, Tzvi attended Bar-Ilan University, studying education and Jewish history. He then became principal of a comprehensive high school, then an educational superintendent in the Ministry of Education and Culture.
He and Ruthie had three sons and numerous grandchildren.
Tzvi published Lehi, From Nothing, To Where? and Land of the Dove and Gazelle.
As of late 1993, as Anshel Shpilman fell ill, he became active in Beit Yair. At the time of his death, he was the director of the Freedom Fighters of Israel Heritage Association.