He was promoted to the first-team squad in March 2016 and he also signed a new professional contract until 2018.[6]
Skovgaard left Nordsjælland at the end of his contract, which was at the end of 2018.[7] This was announced on 18 December 2018.
On 5 February 2020, it was announced that Skoovgard will go on a season long loan to Swedish club Örebro SK in Allsvenskan.[8] After returning to Heerenveen, his contract was terminated by mutual consent on 1 February 2021.[9]
On 12 February 2021, Örebro SK announced that they had signed Skovgaard permanently on a two-year deal.[10]
On 27 February 2022, he signed for Norwegian club SK Brann with a contract lasting until the end of 2024.[11] In February 2023 he moved to Stabæk.[12][13]
On 29 August 2023, Skovgaard joined Polish Ekstraklasa club Cracovia on a three-year deal.[14]