NSW Police are seeking the extradition of a man arrested in the Caribbean over the alleged murder of a Sydney woman earlier this year.

Key points: Kimberley McRae's body was discovered in January, about a week after she was last seen

Kimberley McRae's body was discovered in January, about a week after she was last seen A 20-year-old man was arrested over her murder on the Caribbean island of Aruba last week

A 20-year-old man was arrested over her murder on the Caribbean island of Aruba last week NSW Police confirmed they were seeking to have the man extradited to Australia

Sex worker Kimberley McRae, 69, was last seen in the Harbour City's eastern suburbs on January 7.

Her body was discovered in the Coogee flat she lived alone in seven days later after her family raised concerns.

Police believe it had been there for some time.

A 20-year-old Colombian student was last week arrested on the island of Aruba — a Dutch territory off the coast of Venezuela — in connection with Ms McRae's death.

A NSW Police spokesperson said: "Detectives from the State Crime Command's Homicide Squad are working with Commonwealth agencies to seek the man's extradition to Australia."

Australia and the Netherlands have an extradition treaty.

Ms McRae — who also went by several other names — lived on Mount Street in Coogee.

Kimberley McRae lived alone in an apartment on this street in Coogee. ( Supplied )

Police described her as well known in the area, and said she was "often seen" around the beach-side suburb.

At the time her body was discovered, Detective Superintendent Danny Doherty said police were pursuing Ms McRae's employment as a sex worker as one line of inquiry.

"Kim had a distinct personal style with recognisable features and a wide circle of associates," he said.

"Investigators are aware Kim worked in the sex industry and may be known to some of her associates as Isabella, Samantha and Sabrina."