Mitspa Onyoka fired his legal aid attorney on Tuesday, when he was due to apply for bail in Cape Town Magistrate's Court.
His case was postponed until March 22 to give him time to consult his new lawyer.
The 24-year-old Congolese national allegedly stabbed Curran, 60, to death in his Buitengracht Street apartment on November 7 2018.
Video footage from the apartment block lifts are said to show Onyoka entering and exiting the building at times which coincide with the murder.
Curran worked for Mellon Education, an NGO which helps governments improve the performance of under-resourced schools.
TimesLIVE reported last year that Onyoka worked as a cleaner at a business in Voortrekker Road, Cape Town, where he was arrested.
Curran had just completed a two-year directorship contract in South Africa and was taking an extended vacation.
