From January 2019 until July 2021, Dame Clare was chair of the General Medical Council, the first woman appointed to that role.

[2] Her surgical house jobs were in the London area and later she completed arthroplasty training at Brigham and Women's Hospital in Boston, Massachusetts, in the United States.

In 2013 she became associate medical director at Ipswich Hospital NHS Trust with a special remit for revalidation and appraisal and continued in that role, having stopped active orthopaedic practice in March 2014.

[8] After the United Kingdom voted to leave the European Union in the June 2016 referendum, Marx posited in an interview with The Daily Telegraph that Brexit was an opportunity to improve safety standards in the NHS by strengthening medical device legislation and language testing for non-British workers.

[9][10] The Royal College of Surgeons of England later sent out a press release clarifying that they did not endorse a return to excessive hours for NHS workers.