Born in Palermo, capital of Sicily, Italy, Zerbo is a youth product of U.S. Città di Palermo, one of the Serie A clubs on the island at that time. Zerbo spent the 2008–09 season in the national junior league with Palermo's under-15 team. He was a member of the Palermo under-17 team in the Campionato Nazionale Allievi Professionisti during the 2009–10 and 2010–11 seasons. Zerbo made his professional debut on 15 December 2010 against Lausanne, despite he was the last minute substitute for Massimo Maccarone. Zerbo also played for the reserve team since 2010, which he became a full member in 2011–12 season. Zerbo scored 8 times for the reserve team before he left the club in mid-2012. On 9 July 2012 Zerbo was farmed to Teramo in co-ownership deal for a peppercorn fee of €500. However, in mutual consent with Palermo, Chievo acquired half of the registration rights from Teramo also for a peppercorn on 31 August. Zerbo did not play any competitive match for Teramo before he left the club. He played once in a friendly match however, as a sub of Righini. On 26 January 2013, Palermo bought back Zerbo as well as bought Stefano Sorrentino from Chievo for a total of €4 million in 2½ year contract and ½+3 year contract respectively. Zerbo spent the entire 2012–13 season with the reserve of Chievo and Palermo.
On 15 July 2013 Zerbo and Stefano Cerniglia were signed by Pergolettese of the fourth division. They also signed a new 3-year young professional contract with Palermo. Zerbo started his fully professional season in the first two games of Lega Pro cup. Zerbo made his league debut in the second round of 2013–14 season as a substitute. On 1 February, Zerbo was signed by FeralpiSalò of the third division.
FeralpiSalò
FeralpiSalò signed Zerbo outright on 11 July 2014 in 2-year contract.
Fermana
In June 2018, after just one year with Francavilla, he signed for Serie C club Fermana for an undisclosed fee.
On 2 September 2019, he joined Carpi on loan for the 2019–20 season. He returned from loan on 15 January 2020 after only appearing on Carpi's bench twice.
