Azur started his career as a sportswriter for Hadashot.[2]
Azur is the owner of advertising rights for Israel Plus.[2] With Pini Zahavi, he also runs Charlton, a company which owns broadcasting rights for football matches in Israel.[3][4]
Through Mirkaei Tikshoret, he runs radio stations in Israel and The Jerusalem Post.[2] Canadian investor Leonard Asper sued for a controlling stake in the Post in 2005 after failed negotiations with Azur. The lawsuit was dismissed in 2006.[5][6][7] He co-owned the Israel Post, which started publishing in 2007. In 2012, he launched Sof Hashavua, a newspaper only published on Fridays.[2] In 2014, he acquired Maariv, another Israeli newspaper.[8] In 2020, he bought the Walla! internet portal from Bezeq.[9]