Son of former Reus player Kiko Alabart, Ignacio was born in La Coruña and began playing for the Compañíade María club at the age of five. After training at La Masia Blaugrana, he made his first team début at the age of 17, at a Barça-Blanes game in OK Liga. His début at the Euroleague came in 2015 against the Dinan Quevert hockey club. Following an excellent performance with Barça B during the 2014/15 season (33 goals in First Division) and being crowned junior champion of Catalonia and Spain, Alabart transferred to the CP Voltregà hockey club to play his first full season in OK Liga. In Sant Hipòlit, he played two seasons, got experience and proved his worth for the highest state-level competition. His return to the original Blaugrana team came in the summer of 2017, after becoming one of the model players for his team and scoring 26 goals in the 2016/17 OK Liga.