In 2007, Zec signed for Šibenik where he quickly established himself in the first team. He was voted best young Bosnian player of the year in 2009 by journalists. In a voting where all the captains in the Croatian League participated, Zec was voted the best player of the league in 2009.

Zec made his senior international debut on 19 November 2008, in a friendly match against Slovenia.

In June 2010, he signed a four-year contract with Turkish club Gençlerbirliği.

On 29 May 2010, he scored his first goal for the national team in a 4–2 loss against Sweden.

After four years in Turkey, in September 2014, Zec returned to Croatia, signing with Rijeka.

On 27 July 2015, je signed a one-year contract with Gabala in the Azerbaijan Premier League, with the option of an additional year. On 21 May, Gabala announced that Zec was leaving the club.

On 26 August 2016, Zec signed with Turkish Süper Lig club Karabükspor. During August 2017, he left Karabükspor.

On 25 August 2017, he signed with Gazişehir Gaziantep in the TFF First League. On 10 August 2018, it was announced that Zec left Gazişehir Gaziantep.

On 21 January 2019, he signed a contract with Bosnian Premier League club Željezničar. He scored his first goal for Željezničar on 3 March 2019, in a 2–1 home league win against Mladost Doboj Kakanj. Zec extended his contract with Željezničar for three more years on 18 June 2019, which is due to keep him at the club until June 2022. On 24 August 2020, it was confirmed that he, alongside five other Željezničar teammates tested positive for COVID-19, amid its pandemic in Bosnia and Herzegovina. Only four days later, on 28 August, Zec tested negative for the virus.