Born in the Faroe Islands, he moved to Copenhagen in August 2012, where he swims at the Danish National Training Centre.

Pál Joensen won 3 gold medals at the 2008 European Junior Swimming Championships in Belgrade.

Pál Joensen won gold and set several Faroese records at the 2009 Island Games in Åland: At the 2009 World Aquatics Championships in Rome, Italy, Joensen competed in all three events – 400 m, 800 m, and 1500 m. He did not proceed past the heats stage in any of the events.

[20] At the World Cup in Moscow, on 7 November 2009, Pál Joensen won the men's 1500 metre freestyle (14:32.64) short course (25 m), beating his own national record of 14:39.99 set in December 2008.

He also broke the Nordic record, which was set by the Dane Mads Glæsner at the World Cup in Stockholm 2008.

[21][22] At the World Cup in Stockholm, on 11 November 2009, Pál Joensen won silver in the men's 1500 metre freestyle short course (25 m); his time was 14:32.59, which was new Nordic record.

[23] On 15 November 2009, Pál Joensen won silver in the men's 1500 metre freestyle short course (25 m) at the World Cup 2009 in Berlin.

The gold medallist in the race was Jan Wolfgarten, from Germany, who swam a time of 14:20.44, silver was won by Federico Colbertaldo, from Italy, and the bronze medal by Mads Glæsner, from Denmark.

[26] A few days later, on 17 April 2010, Joensen swam in the final in 1500 metre freestyle for men; he was number three with the time of 15:21.84.

[27] Pál Joensen participated in the British Gas Great London Swim 2010, which was held on 3 July 2010.

The results for the three first swimmers: Pál Joensen won two silver medals at the World Cup in Berlin in October 2010.

[32] Pál Joensen won two gold medals in Moscow at the 2010 FINA Swimming World Cup.

Pál Joensen swam in the final of the men's 400 metre freestyle at the 2010 FINA Swimming World Cup in Stockholm on 6 November 2010.

Pál Joensen participated in 15 swimming events at the 2011 Islands Games on Isle of Wight in the period 25 June to 1 July 2011.

On 26 July, he made it to the finals in 800 metre freestyle with the second best time 7:45.55, which was new Faroese and Nordic record.

Joensen qualified for the 2012 Summer Olympics, fulfilling a career dream, by swimming 25 seconds under the qualification time, which was 15:11.83.

On 15 and 16 October 2011, Pál Joensen participated in two events in World Cup in Stockholm, Sweden.

[43] In December 2011 Joensen participated in the 2011 European Short Course Swimming Championships, which was held in Szczecin, in Poland.

His results: In December 2012 Joensen competed at the World Swimming Championships on short course in Istanbul.

[52] Drug testing later revealed that Glæsner committed a doping violation at the meet, and was stripped of his medals in Istanbul in June 2013, elevating Joensen to silver in the 1500 m.[53] However, upon appeal to the Court of Arbitration for Sport, Glaesner's 1500 metre freestyle gold medal was reinstated based on the fact that a test after that race, two days after his initial positive test following the 400 metre free, was clean.