The incident comes after Kelston Boys High School, Kelston Girls College, Kelston Intermediate School and St Leonards Rd School all went into lockdown shortly after 2pm yesterday.
Police were armed and by 6pm had found the person they were looking for.
St Leonards Rd School was also put in lockdown this week.
Brinsden said they were notified of this morning's incident immediately by police and their lockdown procedures kicked in, which included notifying parents by text message.
"The police were in pursuit of a car that came onto our campus and the occupants abandoned the car in the back car park and we were notified by police and placed into lockdown.
"Staff and students all followed the appropriate procedures following the announcement. We sent out a text message to parents to alert them of the situation."
The school was currently in the midst of its award ceremonies this week but all students were safe as they were in class at the time the incident happened.
"All parties were safe, police notified us as soon as possible. We're really pleased with the way the police responded and our staff and students responded to ensure the safety of all.
"Parents were assured that everyone was safe in the text message that went out."
The lockdown was lifted after about 20 minutes.
Brinsden said she wasn't sure of the exact movements of the car's occupants at their school but she imagined police were hot on their heels.
"It appeared to be quite a low risk but we were put into the right procedures to ensure the safety of all."
Given all students had their phones with them at school, albeit in their bags, she said the school was keen to message parents early on to ensure the correct information was being distributed.
