Noel was appointed as a lay member to the Judicial Appointments Commission in February 2012, was re-appointed for a further 3 years on 1 February 2014, and re-appointed for a further 2 years and 6 months on 1 February 2017.

Noel was vice-chancellor of Aberystwyth University from 2004 until his retirement in 2011. He a member of the Commission on the Devolution of Wales (the Silk Commission), chair of High Performance Computing Wales and also chair of Fair Trade Wales. An academic mathematician, he has worked in Aberystwyth since 1974 after an early career in Cambridge, becoming pro vice-chancellor in 1997. He has also been chair of Higher Education Wales, vice president of Universities UK and board member of the Quality Assurance Agency for Higher Education.