On 31 January 2020, Domgjoni joined TFF First League side Menemenspor, on a two-and-a-half-year contract. On 10 February 2020, he made his debut in a 2–2 away draw against Akhisar Belediyespor after being named in the starting line-up.

On 31 January 2019, Domgjoni joined Albanian Superliga side Laçi, on a two-year contract. On 17 February 2019, he made his debut in a 1–0 home win against Partizani Tirana after coming on as a substitute at last minutes in place of Regi Lushkja.

On 11 July 2019, Domgjoni commenced his second season with the club by playing in the first qualifying round of 2019–20 UEFA Europa League against the Israeli side Hapoel Be’er Sheva after being named in the starting line-up and becoming the team’s key player for the rest of the season.

On 8 August 2018, Domgjoni joined Albanian Superliga side Kastrioti, on a one-year contract. On 18 August 2018, he made his debut in a 0–1 away win against Luftëtari after coming on as a substitute at 61st minute in place of Juljan Shehu.

On 18 January 2018, Domgjoni received a call-up from Albania U20 for the unofficial friendly matches against Azerbaijan U21, he was an unused bench in that matches.

On 24 August 2017, Domgjoni joined Football Superleague of Kosovo side Liria, on a season-long loan.

On 22 January 2016, Domgjoni joined Albanian First Division side Kastrioti, on a six-month loan. On 13 February 2016, he made his debut in a 3–0 home win against Ada after being named in the starting line-up.

On 4 August 2016, Domgjoni received a call-up from Albania U21 for the friendly match against Italy U21, he was an unused bench in that match.

On 4 October 2015, Domgjoni made his debut in a 2–3 home defeat against Egnatia after being named in the starting line-up.

On 5 March 2015, Domgjoni was named as part of the Albania U19 squad for Roma Caput Mundi. On 9 March 2015, he made his debut with Albania U19 in a match against Malta U19 after being named in the starting line-up and scored own goal during a 0–1 home defeat.

On 2 July 2014, Domgjoni signed his first professional contract with Albanian Superliga side Tirana after agreeing to a five-year deal. On 1 October 2014, he made his debut with Tirana in the first round of 2014–15 Albanian Cup against Sopoti after being named in the starting line-up.

Domgjoni was born in Prizren, FR Yugoslavia from Kosovo Albanian parents. On 18 February 2014, he obtained Albanian passport.

In December 2012, Domgjoni received a call-up from Albania U17 for a selection camp in Pristina, Kosovo from 3–4 December 2012. On 23 March 2014, he was named as part of the Albania U17 squad for 2014 UEFA European Under-17 Championship elite round. On 26 March 2014, Domgjoni made his debut with Albania U17 in a 2014 UEFA European Under-17 Championship elite round match against Italy U17 after being named in the starting line-up.

David Nue Domgjonas (born 21 May 1997), commonly known as David Domgjoni is an Albanian professional footballer who plays as a centre-back for Turkish club Menemenspor.