Denise Adderley, 39, was shot six times while sitting inside her car at the Texaco Service Station at Wulff and Kemp Roads on Sunday evening.
Police are questioning a 37-year-old taxi driver who allegedly had a relationship with the deceased.
A shotgun was found in the taxi bus. The driver of the taxi is a resident of Hillside Park.
Ms Adderley lived in Chippingham with her mother, sister and young daughter. She was a teacher at Uriah McPhee Primary School.
Classes at the school were suspended and counseling sessions for the students are underway.
Ms Adderley is the third homicide victim of the new year.
