[2][1] Acquaye served as the head of the Haematology department of the University of Ghana Medical School from 1988 to 1990 and also 1994 to 2002, and was the president of the West African College of Physicians from 2003 to 2004.
[6] Acquaye returned to KBTH campus in June 1986 and was posted to the National Blood Transfusion Service (NBTS), of which he became the head towards the end of that year.
Some of the landmark decisions taken during his tenure included ending the annual strike action of housemen by making them sign tenancy agreements, developing an objective format for the assessment of house officers in collaboration with Professor Joe Oliver-Commey (which later became the format used by the Medical and Dental Council), and obtaining financial autonomy for KBTH, freeing it from the control of the Ministry of Health.
[6] In 1987, Acquaye joined the University of Ghana Medical School (UGMS) as a part-time Senior Lecturer in Haematology, a position he held until 1997 when he became a full-time Associate Professor.
[6] Acquaye served as Chairman of the Committee that formulated modalities for income generating activities at UGMS and oversaw its implementation for two years.
He has also chaired committees on functions and management of the Radiation Oncology unit and awards categorization for the 50th anniversary celebration of UGMS.
Acquaye has also been involved in curriculum development, securing clinic time, and advocating for care giver hospitality in the Haematology Department.