He graduated from the historical University of Pristina's Faculty of Economics in 1987 and later received a master's degree from the post-1999 institution of the same name on the topic, "Problems of improving the fiscal system of the Republic of Kosovo."

He worked in the private sector from 1990 to 1998 and led the Mitrovica municipal assembly's directorate of public services from 2000 to 2003.

Hamza was given the fifty-fifth position on the PDK's list in the 2007 parliamentary election and finished in fortieth place among the party's candidates.

Due to a requirement that one-third of seats be reserved for female candidates, he was also not immediately in line for a replacement mandate.

[9] In June of the same year, he and Albanian economy, trade, and energy minister Genc Ruli announced an agreement on cooperation for electrical power.

[11] Hamza said in a 2009 interview that investment in energy, roads, and private sector were necessary strategic steps to boost economic growth in Kosovo.

[14][15] His first term as a legislator as brief; the PDK formed government after the election, and Hamza was appointed as Kosovo's finance minister on the day the assembly convened.

[18] The following year, he signed an agreement with Turkish finance minister Mehmet Şimşek to collaborate on mutual tax relations.

Hamza resigned as governor of the central bank on 13 September 2017 to return to the office of finance minister.

[22] In February 2018, he helped to facilitate a European Union grant of 38.5 million Euros for the upgrade of Kosovo's railway system.