Dr Crompton holds a PhD in Humanities from the University of Natal. After teaching for a year, Dr Crompton joined the Chemical Workers Industrial Union as an organiser. He rose to become the General Secretary of the union as well as a member of COSATU's Central Executive Committee. He was also an executive member of the International Federation of Chemical, Energy and General Workers Union.

Dr Crompton was the Labour Convenor of the National Economic Forum Liquid Fuels Industry Task Force where he played a leading role in shaping policy proposals that led to a number of government policies in post-1994.

In 1994 he was appointed the Director of the Minerals and Energy Policy Centre (MEPC) where he turned the institution into a competent and profitable contributor to energy policy in Southern Africa. It was under Dr Crompton's leadership and guidance that MEETI was launched.

He then joined the Department of Trade and Industry as Director of the Chemical and Allied Industries where he was responsible for import tariffs for all chemical industry products, liquid fuels and electricity. He also oversaw tariff investigations and the development of proposals for EU and SADC Free Trade Agreement proposals.

In 1998 he was appointed Chief Director responsible for Hydrocarbons in the Department of Minerals and Energy and later the Deputy Director-General of the same unit. He led the drafting of the hydrocarbons section of the White Paper on Energy Policy, the White Paper on Renewable Energy and the Strategy for the Refining Petrochemical and Gas Sectors. Dr Crompton was part of the restructuring of the Central Energy Fund Group of companies, including drafting its business strategy. He has also chaired the interdepartmental task team responsible for the restructuring of Petronet. During this time he also sat on the Boards of MossGas, Soekor and iGas.

He has advised the Minister of Minerals and Energy on a number of major policy interventions, such as the drafting of regulations for the liquid fuels industry, drafting the first empowerment charter in the liquid fuels industry, helped negotiate the Sasol Agreement (which is now under NERSA's jurisdiction), drafted the Gas Act, Petroleum Pipelines Act, the National Energy Regulator Act and is currently leading the finalisation of the Energy Bill. Dr Crompton is also the Chairperson of MEETI and has published widely, including a book entitled “An Industrial Strategy for the Commodity Plastics Sector”.

Dr Crompton currently serves as full-time Regulator Member of the National Energy Regulator (NERSA) primarily responsible for petroleum pipelines regulation.