Greif made his professional debut for Slovan Bratislava against MFK Zemplín Michalovce on 13 May 2016.[3] During the 2018–19 season, Greif was the first-choice goalkeeper over Michal Šulla, playing in 29 of the 32 games during the season.[citation needed]
Mallorca
On 6 July 2021, Greif joined newly-promoted La Liga side Mallorca on a five-year contract.[4]
Shortly after his arrival, he was plagued by various health problems:[5] a muscle injury first sidelined him for a month, he then had to fight an infection of his wisdom teeth and he was sidelined by major chronic pain caused by an unspecified illness not related to football. He could not practice for almost a year until doctors finally found the cause and provided appropriate treatment. Greif eventually came back to play in a competitive game in December 2022.[6]
During the 2023–24 Copa del Rey, Greif dropped out of a training camp in Valle de Egüés due to a gastric illness.[7] He returned in the semi-final against Real Sociedad on 27 February 2024, saving a penalty from Brais Méndez in the first half and from Mikel Oyarzabal at the start of the subsequent shootout, which Mallorca won 5–4 to reach the final.[8]
International career
Although Greif was noted as a back-up goalkeeper in the Slovak senior team,[9] he was first called up to the national team on 25 May 2019 by Pavel Hapal. The nomination was for a double fixture in June – a home friendly match against Jordan, to which, unusually, 29 players were called-up and a UEFA Euro 2020 qualifying fixture against Azerbaijan, played away on 11 June 2019. The squad was reduced to 23 players for the latter fixture.[10]
Greif debuted for the Slovak senior squad against Jordan on 7 June 2019 in a 5–1 win at the Anton Malatinský Stadium in Trnava.[11] He came on in the second half as a replacement for Matúš Kozáčik, with Slovakia losing 1–0, maintaining a clean sheet despite only having to face few rather undangerous situations.[12]