Patrik progressed through the Breiðablik academy in Iceland. On 8 June 2018, Patrik moved to England to join the B team at Brentford on a two-year contract, with the option of a further year. On June 2019, Patrik signed a new four-year contract, with the option of a further year and was a part of the first team squad during the majority of the 2019–20 pre-season. He spent the entire 2020–21 season away on loan at Danish clubs Viborg FF and Silkeborg IF, switching clubs during the mid-season transfer window. He made 26 appearances during the season and both clubs secured promotion to the Superliga. In August 2021, Patrik joined Norwegian Eliteserien club Viking on loan until the end of the season. On 17 January 2022, Patrik joined the club on a permanent contract for an undisclosed fee.