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2020–2021: ATP debut

Nardi made his ATP main draw debut at the 2020 European Open in singles, where he lost to Marcos Giron in three sets, and in doubles partnering Zane Khan.

He reached career-high rankings of World No. 356 in singles and No. 544 in doubles on 13 December 2021 after reaching the semifinals in singles and quarterfinals in doubles respectively as a wildcard at the 2021 Città di Forlì III Challenger.

2022: Four Challenger titles, Masters & Top 150 debuts & first ATP win

In the first week of the 2022 ATP Challenger Tour, Nardi won his first Challenger title at the 2022 Città di Forlì Challenger, defeating Mukund Sasikumar in the final. As a result, he reached the top 300 on 17 January 2022 at world No. 296.

He won his second Challenger title at the 2022 Challenger Città di Lugano, defeating Leandro Riedi in the final. He made his Masters debut at the 2022 Rome Masters as a wildcard.

He won his third Challenger title at the 2022 Rafa Nadal Open in Mallorca, beating Zizou Bergs in the final. This was his first Challenger win on an outdoor hard court. He made his debut in the top 150 at world No. 142 on 12 September 2022.

At the ATP 500 2022 Astana Open he qualified into the main draw defeating top seed David Goffin. He won his first ATP match and first at the ATP 500 tour-level defeating fellow qualifier Alexander Shevchenko to reach the second round. He lost to third seed Stefanos Tsitsipas in very close match with two tiebreaks having had two breakpoints, and conceding none.

2023–2024: First Masters and world No. 1 wins & fourth round, top 100

Ranked No. 159, he made his debut at the 2023 Monte-Carlo Masters after defeating fourth seed Constant Lestienne and eleventh seed Oscar Otte in the qualifying competition. He won his first round match, recording his first Masters win and only his second on ATP tour-level, over wildcard Valentin Vacherot. He lost by a double bagel to compatriot and 16th seed Lorenzo Musetti in just 50 minutes. As a result, he moved more than 15 positions up in the rankings.

He received a wildcard for the main draw at the Italian Open, where he lost in the first round to David Goffin. In the following weeks, Nardi reached two Challengers quarterfinals, in Vicenza and in Milan. In August, he won his fourth Challenger title in Porto, defeating Portuguese João Sousa in the final and reached a career high ranking of No. 116 on 28 August 2023. In October, he received a wildcard for the main draw of the 2023 European Open. In November, he qualified for the 2023 Next Generation ATP Finals.

Ranked No. 123 at the 2024 BNP Paribas Open he replaced as a lucky loser, 30th seed Tomás Martín Etcheverry directly into the second round. He defeated Zhizhen Zhang for his first win at this Masters and reached his first third round at this level. In his next match, he took the first set off world No. 1 Novak Djokovic the first lucky loser to do so at an ATP Masters 1000 event, and the first at an ATP event overall since fellow Italian Lorenzo Sonego in Vienna 2020. He ended up winning that third round match in three sets against the top seed to reach the fourth round for the first time in his career and became the lowest-ranked player ever to defeat Djokovic at a Masters or a Grand Slam. As a result he made his top 100 debut in the rankings.