FC Khimki

Kvirtiya joined FC Khimki in August 2002. In the Winter Cup semifinals came off the bench and scored two goals against Russian Premier League team FC Saturn, his team won 4-3 but in the final he couldn't get his first trophy with the team and they lost 0–1. He scored 3 goals in the second season for FC Khimki.

AZAL

On 7 July 2009, Kvirtiya signed a 2-year contract with AZAL PFC. Kvirtia made his Azerbaijan Premier League debut against Neftchi Baku on 16 August 2009. In his debut season, his team could not get into the top six. In the end of 2010, FC Gabala was interested in him but AZAL PFC didn't sell him.^[1]

The next season 2010/2011 for Kvirtia was one of the best; AZAL PFC get into the top six. In the quarter-final of the Azerbaijan Cup he scored at 43 minutes and AZAL PFC reached the semifinal. After a minor injury, he returned on 16 October 2010 as a substitute in the match against Inter Baku when the score was 0-0, he made an assist and then scored himself. AZAL PFC won at the defending champion 5–0. Kvirtiya become one of the best pass assistants in the team.

In the season 2010-2011 Kvirtiya helped his team to get into the qualifying round of the UEFA Europa League. On 30 July 2011 Kvirtiya made his debut in the UEFA Europa League against FC Minsk, when he came on as a substitute in the 71st minute. The first game ended with the score 1–1 in Baku. The second game was in Minsk and AZAL PFC lost 1-2 and flew out of the UEFA Europa League.

Turan Tovuz

Kvirtiya signed a one-year contract with the Azerbaijan team.^[2] Asker Abdullayev invited him in Turan Tovuz, who had worked with him in the 2009/2010 season in AZAL PFC. Abdulayev initiated Kvirtiya's move from Russia and he gave him the number 10 shirt in AZAL PFC, but in Turan PFC he played with number 25 because the shirt with number 10 was the captain of the team. On 23 September 2012 he played his first match in new team against Qarabağ FK. Kvirtiya bring some creative in Azerbaijan Premier League celebrating team goals with his teammates.^[3]

FC Guria

14 years have passed since the Kvirtiya playing at home in Georgia, he always wanted to return to his homeland, he signed a one-year contract with FC Guria Lanchkhuti (Umaglesi Liga), in 1980s in the Soviet Union, his father played for this team.^[4] On 2 March 2014 debuted in Georgian Umaglesi Liga against FC Tskhinvali he came on as a substitute in the 65th minute. His team get into the top six and they fought for a place in European competition. During the season 2013/2014 Tarlan Akhmedov head coach of Azerbaijan club AZAL PFC where Kvirtiya was played 3 season wanted to return him, but Kvirtiya moved to Tunisia^[5]

Esperance Sportive de Zarzis

On 7 August 2014 Kvirtiya signed a two-year contract with ES Zarzis, becoming the first Georgian professional footballer to play in the Tunisian Ligue Professionnelle 1^[6] Kvirtia made his debut on 19 August 2014, coming on as a substitute in the 78th minute when the score was 0-0, and helped the team win the first match of the season away against CS Hammam-Lif 1–0.

AZAL

On 28 July Kvirtiya return to his former team AZAL,^[7] signing a one-year contract. He always wanted to come back in his "family team" as he called in all interviews.^[8][9] His first game in the season 2015/2016 was on 9 August against Zira FK. AZAL PFC started the season very badly, but on 2 October Kvirtiya scored his first goal in the championship against Ravan Baku FK and bring the first victory to AZAL PFC 1–0.^[10] His second goal scored against Neftchi Baku from the penalty spot and AZAL PFC won 2–1.^[11] In the season 2015/2016 Nugzar Kvirtiya became the teams's best scorer with 7 goals in Azerbaijan Premier League and one goal in CBC Sport Cup. Next season 2016/2017, Nugzar once again becomes the team's top scorer.