Fatos Hoxha and the municipality of Kukës hired Shahin Berberi as the club's manager and gave him the financial backing to make many signings in order to achieve promotion.

[9] FK Kukësi's first European game was played on 4 July 2013 and it ended in a 1–1 draw away at Estonian side Flora Tallinn, with midfielder Gerhard Progni scoring a 79th-minute equaliser.

[10] The return leg was played at the Qemal Stafa Stadium in Tirana and it ended in goalless draw which meant that FK Kukësi progressed to the second qualifying round of the Europa League on the away goal rule.

[12] In the second leg played at the Asim Ferhatović Hase Stadium, the match ended goalless which meant FK Kukësi progressed to the third and final qualifying round of the competition.

[14] FK Kukësi experienced their first European defeat in their sixth fixture at the hands of Metalurh Donetsk in the away leg of the tie, but still progressed through to the play-off round as they won 2–1 on aggregate over the two games.

[16] At the Hüseyin Avni Aker Stadium in the second leg FK Kukësi managed to open the scoring through Lazar Popović in the 11th minute, before conceding three times to lose 5–1 on aggregate.

They lost their following game against Partizani Tirana which resulted in the head coach Armando Cungu being replaced by Naci Şensoy,[18] whose reign at FK Kukësi began with two draws and a loss that landed the club back in the relegation zone.

However, the head coach Şensoy was under pressure from both the fans and the president Safet Gjici, and after winning just once in his next four league games he resigned immediately after a goalless draw at home against Bylis Ballsh.

[21][22] Starova began with a disappointing 2–0 loss to relegation bound Besa Kavajë, before beating Flamurtari Vlorë and KF Laçi consecutively to regain some momentum for a late title push.

They also had a strong Albanian Cup run, as they eliminated Naftëtari Kuçovë, Apolonia Fier, Bylis Ballsh and Teuta Durrës to reach the final with Flamurtari Vlorë which they eventually lost 1–0 to an Arbër Abilaliaj goal.

The ground was given the name Zeqir Ymeri in honour of a former footballer for the club, and the opening of the stadium was on 30 November 2010, where a friendly was played against Partizani Tirana, which FK Kukësi won 1–0.

The club is well supported in the local community of Kukës as well as the surrounding regions in the north-east, and the main ultras group is called the Armata e Veriut, which translates to the Army of the North.

The supporters have been known for some negative behaviour, which included a top of the table clash with Luftëtari Gjirokastër on 6 May 2012 in the Albanian First Division, where the FK Kukësi fans were seen throwing object onto the field which resulted in the referee Lorenc Jemini having to pause the game.

The club was fined a total of €27,000 for the behaviour of its supporters during their Europa League run in the summer of 2013, as they threw bottles and flares onto the field of their home games against Sarajevo and Metalurh Donetsk.