[1] Brobbey was called to the bar in 1967 and begun private legal practice for some time before joining the Council for Law Reporting.
In 1981 he joined the Zimbabwean Judiciary as a legal consultant under the auspices of the Commonwealth Trust Fund Technical Co-operation.
Upon his return to Ghana from his stint in Zimbabwe in 1986, he was appoint a high court judge.
[3] He resumed his post as a justice of the supreme court of Ghana from 2006 until his retirement on 23 May 2012.
[1] In 2018 he was made chairman of the board of governors of the Economic and Organised Crime Office (EOCO),[4] that same year he was appointed by the government of Ghana to chair the Commission of Inquiry into the creation of new regions.