Born in Urduliz, Biscay, Basque Country, Elgezabal graduated from Danok Bat CF's youth setup.

[4] In the 2016 winter transfer window, Elgezabal refused an offer from RCD Mallorca[5] and remained at the Fabriles until the end of the campaign.

On 20 June 2016, he signed for La Liga side SD Eibar,[6] being loaned to AD Alcorcón in Segunda División on 18 August.

[12] On 10 September 2020, Elgezabal terminated his contract with Alcorcón,[13] and signed for third division side Burgos CF fourteen days later.

[14] On 18 June 2024, after four seasons as a starter for the latter which included a promotion to the second division in his first year, he joined Levante UD on a one-year deal.