Colombian student arrested in relation to Coogee woman's murder to be extradited back to Australia

A South American student has been arrested in relation to the death of a woman in Sydney's eastern suburbs earlier this year.

The body of 69-year-old Kimberley McRae was found in her apartment on Mount Street in Coogee on January 14.

Ms McRae was well-known in the area and was often seen running along the foreshore in the evenings before her alleged murder.

Last week, a 20-year-old man was arrested in Aruba, an island off the coast of Venezuela, in relation to Ms McRae's death.

NSW Police said in a statement it was "aware of the arrest" and is working to bring the Colombian man back to Australia.

"Detectives from the State Crime Command Homicide Squad are working with Commonwealth agencies to seek the man's extradition to Australia," it said in a statement.

"The priority for Australian authorities is seeking the return of the man to face justice."

Ms McRae lived on her own and did not have a car but was known to walk and exercise in the local area. She was also known as Isabella, Samantha and Sabrina, worked in the sex industry, police said.

"She was quite a distinct sort of person, everyone recognised her and if you saw her, you would know her," Detective Superintendent Danny Doherty said just after her death.