Constance stood as a candidate for Depute leader of the SNP in the party's 2014 leadership contest, but lost to Stewart Hosie.
Constance was born in Blackburn, West Lothian, the daughter of Simon Constance, a coalminer, and Mary Constance (née Colquhoun). She was raised in Addiewell and West Calder. While studying at the University of Glasgow, Constance was elected President of Glasgow University Students' Representative Council, where her sabbatical vice president was Alasdair Allan, now SNP MSP for the Western Isles.
Before her election to Holyrood, Constance worked as a social worker and was a councillor for West Lothian Council where she was the SNP spokesperson for children's services and lifelong learning. She also stood for the SNP in the Livingston by-election, 2005.
During the 2014 SNP spring conference, First Minister and SNP leader Alex Salmond promoted Constance to the Scottish Cabinet in the position of Cabinet Secretary for Training, Youth and Women’s Employment. In the position, Constance was somewhat criticised by the opposition Scottish Labour Party in the Scottish Parliament, claiming that since Constance, youth unemployment in Scotland had actually risen. In response to this, Constance stated:
These figures, based on data for 2013, show that the employment prospects are improving across much of Scotland, with women’s employment driving much of this improvement. “They also show that Scotland continues to outperformed the UK across all headline labour market indicators, with a lower unemployment rate, higher employment rate and lower economic inactivity rate.
Previously, Constance was a junior Scottish cabinet member.
Following defeat in the Scottish independence referendum, 2014, Scottish National Party leader and First Minister of Scotland Alex Salmond announced his resignation as SNP leader and First Minister of Scotland. In the aftermath of his resignation, a leadership bid was launched, and current Deputy First Minister of Scotland and SNP Depute leader Nicola Sturgeon was widely tipped to become Salmond's successor.
On 30 September 2014, Constance officially launched her bid to become the Depute leader of the Scottish National Party, competing against Stewart Hosie and Keith Brown. It was later revealed by Constance that she was "not seeking the position of Deputy First Minister".
The results of the election were announced at the SNP Autumn Conference on 14 November, with Constance losing the contest to Stewart Hosie, after being eliminated in the first round.
Following the election of Nicola Sturgeon as the First Minister, in November 2014, Constance was promoted as the Cabinet Secretary for Education within the Scottish Cabinet.
After the 2016 Scottish Parliament election, Nicola Sturgeon reshuffled her Cabinet. On 18 May, Constance was appointed as Cabinet Secretary for Communities, Social Security and Equalities.
After her election to Holyrood, Constance announced she was expecting her first child in October 2007.