Born in Galdakao, Biscay, Basque Country, Zarrabeitia joined Athletic Bilbao's Lezama academy in 2009, from SD Amorebieta.
Upon returning, Zarrabeitia was assigned to the main squad of the Azules in Segunda División B for the 2013–14 season,[1] but featured rarely before moving on loan to JD Somorrostro in January 2014.
[3] On 13 January 2018, after failing to play a single minute for Amorebieta during the first half of the campaign, Zarrabeitia returned to Zamudio on loan until June.
[4] He returned from loan in July 2018, and was mainly used as a backup to Aitor Aldalur as his side achieved a first-ever promotion to Segunda División in the 2020–21 campaign.
Zarrabeitia made his professional debut at the age of 28 on 25 September 2021, coming on as a second-half substitute for Iker Bilbao in a 0–1 away loss against CD Leganés.