After joining the Scottish National Party in 1997, aged seventeen, Grady stood at the 2010 general election as the SNP candidate for Glasgow North.

[6] Like several SNP MPs and MSPs, he also holds membership of Plaid Cymru, although this has no formal effect in the House of Commons, as he was not elected to represent that party.

[8] In December 2021, a woman was convicted of an offence under section 127 of the Communications Act 2003 after a sheriff determined that emails that she sent to Grady in February 2021 were grossly offensive.

The report stated "The distinction in age, status and authority between him and the respondent is obvious and forms a key aggravating factor in the case.

"[16][17] In the same month, a report from the Independent Expert Panel published advice that Grady should be suspended from the House of Commons.

[27] On 12 October 2023, Lisa Cameron MP defected from the Scottish National Party to the Conservative and Unionist Party in the House of Commons, hours before the result of her selection contest was to be announced, claiming that she had been "ostracised" by the SNP after claiming to have previously spoken out over the handling of misconduct by Grady.