Taberner made his ATP Tour debut at the 2018 Open Sud de France in Marseilles where he advanced through 2 qualifying matches to reach the main draw.

In qualifying, he defeated Benjamin Bonzi 6–2, 6–4 and Marco Trungelliti 4–6, 6–2, 6–4, where he then won his first round match against Norbert Gombos in two tie-breakers 7–6(7–5), 7–6(7–1).

He made his Grand Slam debut in the main draw at the 2018 French Open as a qualifier where he lost to Stefanos Tsitsipas.

He won his third Challenger title at the 2021 Open du Pays d'Aix defeating Manuel Guinard.

He also entered directly into the main draw for his second Masters 1000 of the season and in his career at the 2021 BNP Paribas Open in Indian Wells and made it to the second round, recording his first win at this level by defeating fellow Spaniard Jaume Munar.

In February 2023, he made the main draw as lucky loser in Santiago, Chile after the withdrawal of Bernabé Zapata Miralles.