Grace Fisher, 16, was reported missing on Friday 13 October 2023.
Since her disappearance, officers have carried out extensive enquiries to find her but have been unable to do so.
On Thursday 2 November a local man in his 20s was arrested in connection to the case. He remains in custody at this time.
This man is believed to have been with Grace near Chatham Bus Station, at around 10.30pm on the same day she was reported missing. They were then seen again on CCTV walking in The Brook at around 11.30pm.
Detective Inspector Scott Relf said: ‘This is the second arrest we have made in connection to the investigation. A man who was previously arrested remains on bail.
‘Grace if you are reading this then I want to encourage you to get in touch with us, we want to ensure you are safe and remind you that you are not in trouble.’
Grace was last seen wearing a grey jumper with a black ‘New York‘ emblem, black leggings and white Nike trainers. She sometimes uses the names ‘Rosie’ or ‘Harmony’.
She has links to Medway, Maidstone and also Camden in London.
Anyone with information who has seen Grace or knows where she is should call 999, quoting reference 13-1191.