Born in Odense, Hyllegaard started his senior career at SfB-Oure FA in the Denmark Series, the fifth tier of the Danish football league system, where he developed into a prolific goalscorer.
[3] On 28 December 2019, Odense Boldklub (OB) signed Hyllegaard to a three-year contract.
[6] In December 2023, to get more minutes in the legs, Hyllegaard - together with his teammate, Mads Hansen - joined Middelfart Boldklub on loan until the end of the season.
[8] This was in the wake of Hyllegaard having trained with Faroese club HB Torshavn during January.
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