David graduated with honours from Glasgow University in 1987.
In 1997, he set up his own practice, Taylor & Kelly, which subsequently became the leading firm for issues arising from prisoner's rights. In 2004 he was granted rights of audience in the High Court of Justiciary. Subsequently based in Edinburgh, he practised extensively in the Court of Appeal before joining Crown Office in 2012 as an Advocate Depute, where he served until 2019. During his time as an Advocate Depute, David prosecuted exclusively in the High Court, including drugs, rape and murder cases.