Griffiths was the secretary of John Marek, who represented Wrexham as a Labour member of the Welsh Assembly. However, in 2003 Marek was de-selected by the local party and Griffiths was selected in his place. There followed a Labour Party inquiry, in which Marek was first contacted by telephone half an hour before the result was announced, and his de-selection was upheld. Marek then decided to fight to retain his seat as an Independent,^[9] and Griffiths struggled during the campaign; an early poll showed Marek beating her by 40% to 29%.^[10] In the event, on polling day Marek beat Griffiths by 973 votes.

Having been a supporter of Wrexham Football Club, Griffiths was elected to the board of the Wrexham Supporters Trust. In December 2005 she was selected again as Labour candidate for the Wrexham constituency for the 2007 Assembly elections. She benefited from high-profile support as the party saw an opportunity to recapture the seat; John Marek appealed to the large Polish immigrant population by translating his election material into Polish.^[11] However, Griffiths increased her numerical vote while Marek's vote fell, and she won the seat by 1,250.

In 2011, Griffiths faced Marek for a third time, though by now Marek had joined the Conservatives. Both of them saw increases in their votes compared to 2007, but Griffiths held the seat with an increased majority of 3,337.^[12] Griffiths was re-selected to defend her seat at the 2016 election.,^[13] and retained it with a reduced majority of 1,325 over the Conservative candidate.^[14]

Griffiths was appointed Deputy Minister for Science, Innovation and Skills in December 2009.^[15] After the 2011 election, she was promoted to the Minister for Health and Social Services, a post she held until March 2013 when she was appointed Minister for Local Government and Government Business. In September 2014 she was appointed Minister for Communities and Tackling Poverty.^[7] She was appointed Cabinet Secretary for Environment and Rural Affairs following re-election in May 2016,^[5] before being appointed Cabinet Secretary for Energy, Planning, and Rural Affairs in November 2017. She became Minister for Environment, Energy, and Rural Affairs in the First Drakeford government^[16] in December 2018 and then Minister for Rural Affairs and North Wales, and Trefnydd in May 2021.^[17] In March 2024, Griffiths was appointed Cabinet Secretary for Culture and Social Justice in the Gething government.^[4]

In October 2018 Griffiths used her ministerial office to overturn the decision of a planning inspector to refuse a proposed wind farm near Llandrindod Wells. In November the Campaign for the Protection of Rural Wales announced that it was challenging this in the High Court.^[18]

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