A spokesperson for Sussex Police said Hilary, 52, was last seen in the town on Monday, July 27, at around 7.40pm.
The spokesperson added: “She has long, dark hair and was last seen wearing a black lace vest and orange skirt. It is also believed she may have a small brown dog with her.
“Hilary has links to Crowborough, but it's believed that she is in Eastbourne.
“Officers are concerned for her welfare.
“If you see Hilary or have any information of her whereabouts, please call 999 immediately quoting serial 46 of 28/07.”