[5] Robertson received consistent praise regarding his performances while being such a young age, becoming a first-team regular for the Dee and earning several Man of the Match and SPFL Team of the Week nominations.

Despite his first senior season finishing early due to the COVID-19 pandemic, Finlay was named as Dundee's Isobel Sneddon Young Player of the Year.

On 4 February 2025, Dundee announced that Robertson had signed a new two-and-a-half year deal which would keep him at the club until the summer of 2027.

[17] After an impressive start to his rookie season with Dundee, Robertson earned a call-up to the Scotland U19 squad for two matches against Japan in September 2019.

[18] On 12 October 2023, Robertson was called up to the Scotland U21 squad for the 2025 UEFA U21 Euros qualification group games against Hungary and Malta.