Adept in midfield or as a defender, Holldack began his career in his homeland with Hennef 05, before joining Bundesliga side 1. FC Köln in 2011. He made 78 appearances and scored six goals for the club's U17 and U19 teams and helped the latter side to the Junioren Pokal in the 2012–13 season. He progressed to the club's reserve team in March 2015 and was an unused substitute for three Regionalliga West matches late in the 2014–15 season. Holldack departed the Müngersdorfer Stadion at the end of the 2014–15 season.
Holldack moved to England to sign a two-year Development Squad contract with Championship side Brentford on 1 July 2015. He performed the role of a utility player during the 2015–16 season and scored 14 goals in 31 appearances. After featuring regularly during 2016–17 pre-season, a spate of injuries saw Holldack called into the first team squad for the opening match of the season versus Huddersfield Town. He remained an unused substitute during the 2–1 defeat and made the first senior appearance of his career with a start in the following match, playing at right back in a 1–0 EFL Cup first round extra time loss to Exeter City on 9 August 2016. Despite failing to win a further first team call-up, head coachDean Smith remarked in early January 2017 that Holldack had been "constantly" training with the first team squad. On 20 January 2017, he departed on loan until the end of the 2016–17 season and signed a one-year contract extension on 22 June 2017. After failing to win any further first team call ups, Holldack departed the club on 31 August 2017.
After a period on trial with Sportfreunde Lotte at the club's winter training camp and featuring as an unused substitute during a 3. Liga match, Holldack moved on loan to Regionalliga West club Wuppertaler SV until the end of the 2016–17 season on 20 January 2017. He made his debut with a start versus Fortuna Düsseldorf II on 10 February and scored the first senior goal of his career in the 5–1 victory. Holldack made 13 appearances and scored three goals during his spell at the Stadion am Zoo.
On 31 August 2017, Holldack returned to Germany to join Regionalliga West club KFC Uerdingen 05 on two-year contract. In what remained of the 2017–18 season, he made 26 appearances, scored two goals and celebrated promotion to the 3. Liga after victory in the Regionalliga promotion play-offs. Holldack made 20 appearances and scored one goal during the 2018–19 season and was part of the club's Lower Rhine Cup-winning squad. He was released in June 2019, after making 46 appearances and scoring three goals for the club.
On 2 July 2019, Holldack joined Regionalliga West club Bonner SC on a one-year contract. He made 15 appearances and scored three goals before his departure in January 2020.
VfR Aalen
On 11 January 2020, Holldack transferred to Regionalliga Südwest club VfR Aalen on an 18-month contract. He failed to win a call into a matchday squad before the Regionalliga Südwest season was ended prematurely.
