Slosar joined Swire in 1980 as a management trainee.[6] In 1996, he became managing director of the Hong Kong Aircraft Engineering Company.[6] In 1998, he became managing director of Swire beverages.
In 2011, Slosar became the chief executive of Cathay Pacific. In 2014, he was promoted to Chairman of Swire Pacific, Swire Properties, Cathay Pacific, HAECO, and Swire beverages, becoming the 35th and the first non-British chairman of the company.[7]
In 2015, Slosar was bestowed the Legion of Honour by the French government.[8] He was a director of Air China, PureCircle, and a member of the Council of Lingnan University and the International Advisory Board of Hong Kong Polytechnic University.[9][10]
Slosar stepped down from his chairmanship of Swire in 2018.[11] He stayed on as the chairman of Cathay Pacific until 2019.[12] During the 2019–20 Hong Kong protests, he resisted pressure to suspend employees who participated in the protests and supported the staff's right to protest by saying that “We certainly wouldn’t dream of telling them what they have to think about something.”[13] Slosar resigned in September 2019, before his board term was due to expire in May 2020.[14]