In September 2019 he signed for Burnley following a successful trial. A broken elbow and international clearance delayed his Clarets debut for the under-23 side.[7] He was rewarded with a new contract in January 2020 until the summer of 2021 with the option of a further year, after a string of impressive performances for the under-23 side.[8] He made the bench for the first team on three occasions in June 2020 following the COVID-19 lockdown restart, after it was announced Joe Hart would be leaving the club on a free transfer.[9]
On 1 February 2021, Jensen joined League Two side Bolton Wanderers on loan for the remainder of the 2020–21 season.[10] He played no matches, spending the entire time as second choice behind Matt Gilks. Though he played no matches, he still considered the loan a success as he was able to experience being part of a promotion winning team.[11]
On 14 May 2021, he joined Kórdrengir on loan for two months.[12] He played seven times during this loan spell.
Jensen joined Carlisle United on season-long loan on 20 July 2021.[13] He spent another loan as a back up goalkeeper, playing only four matches total.
On 19 June 2023, Jensen agreed to return to League One when he was announced to have signed for Lincoln City following his release from Burnley.[16][17] On 5 August 2023, he made his Lincoln City debut starting against his former team Bolton Wanderers.[18] He won the EFL Cup players of the second round, saving two penalties in a shootout against Sheffield United.[19] He was given City's Player of the Season Award, following 19 clean sheets in the league during his debut season at the club.[20]
Millwall
On 11 July 2024, Jensen signed for Millwall on a long-term contract for an undisclosed fee.[21] He made his debut on 10 August against Watford, starting the game in a 3–2 defeat.[22]
Career statistics
As of match played 26 December 2024
Appearances and goals by club, season and competition