A woman who had been disqualified from driving until 2063 has been involved in a police pursuit in Sydney's west.

Police say the woman was speeding when they gestured for her to pull over around 3:00am AEST at Castlereagh, west of the city.

A check on the police computer system also indicated the car might be being driven by a disqualified driver.

The driver allegedly sped off and police followed in a chase that reached speeds of up to 150 kilometres per hour in 60 and 80 kilometre speed zones.

The woman hit a power pole at Penrith and was arrested by police.

Officers say they found an amount of the drug ice in the car.

She was taken to hospital for drug and alcohol testing and charged with a range of offences.

She has been refused bail to face court on Tuesday.