After completing the maritime high school, Mišković moved to Norway where he worked at a port and was responsible for controlling the loading and unloading of goods. He continued his career in West Africa, where he initially worked in the port town of Warri in Nigeria for Orlean Invest Holding - a leading logistics corporation in the oil and gas industry. Despite facing difficult working conditions, Mišković soon became the youngest general manager in the company and, through the years, rose to be the executive director.
On 20 March 2012, Mišković rescued Croatian football club Rijeka from debt and threatening collapse, becoming the club's owner and chairman.[8] HNK Rijeka is his hometown club which he has a big fan of from his earliest days. Over the next several years, he transformed the club into a title contender, recording great results both domestically and in Europe. Over the years, Mišković has invested more than 50 million euros into the club and associated infrastructure, which included the construction of a new training camp and a new club stadium named Rujevica. Since Mišković took ownership and puzzled together the management team which still leads the club as of 2025, HNK Rijeka has won a total of seven domestic trophies, becoming champions of the Croatian Football League twice (in 2017 and 2025), and winners of the Croatian Football Cup five times - in 2014, 2017 (with which they secured their first domestic double), 2019, 2020, and 2025 (club's second domestic double).