Fychan worked for 12 years at the
National Museum Wales, serving as Head of Policy and Public Affairs, and was also a lead for governance, strategy, internal communications, international relations and stakeholder engagement. In May 2017, Fychan was elected for
Pontypridd Town ward on
Rhondda Cynon Taf County Borough Council and also Pontypridd Town Council. As a local councillor, Fychan was a vocal community activist. In 2017 she successfully campaigned to reopen Mill Street Post Office and in 2018 she campaigned to save the
Muni Arts Centre in Pontypridd, of which she was a volunteer trustee. In 2020, she dealt with severe flooding in Pontypridd and led calls for an independent inquiry. Fychan was selected in May 2020 to be the Plaid Cymru candidate for the
Pontypridd constituency for the
2021 Senedd election. She came second in the election, behind Labour's
Mick Antoniw, with 22.4% of the vote but was elected to the Senedd from the
South Wales Central regional list. Fychan is the current Plaid Cymru director of
policy and political education. As MS for South Wales Central, Heledd Fychan called for a full investigation into the deaths of two boys after a police chase in
Ely, Cardiff and the events following the incident. Fychan currently serves on the Senedd business committee; children, young people and education committee, and the
Reform Bill committee. She chairs the
Wales International cross party group and is vice-chair of the
Public and Commercial Services Union group. She is further a member of the following cross-party groups: academic staff in universities, arts and health,
autism, children and families, children in our care, clean air, friends of Ukraine, lung health, music, peace and reconciliation, poverty, public transport, school food, tourism, universities, and women. ==Personal life==