Gombachika's father was Brown Chimphamba.[1] He had been an academic, a United Nations diplomat and the University of Malawi's vice-chancellor.[2]
She has published scholarly articles including "HIV and Sexual and Reproductive Health for Couples Living with HIV in Rural Southern Malawi" which she, and others, published in 2013.[3]
In 2017, President Peter Mutharika made a number of important appointments. Wandika Phiri became the head of the county's prisons, Mercy Pindani was made the Principal of the Kamuzu College of nursing and Gombachika became the vice-principal.[4] She and Pindani began their new roles in July 2017.[5]
In 2019, the University of Malawi was reassembled. The college where Gombachika had been vice-principal was merged with the college of Medicine to create a new university.[6] The Kamuzu University of Health Sciences was based in Blantyre, with the President as vice-chancellor.
In March 2023, President Lazarus Chakwera made Gombachika the new Deputy Vice-Chancellor of Kamuzu University of Health Sciences[1]