Police are searching for John Henry Bond, who is wanted in connection with serious harassment and stalking offences.
Police said the 63-year-old pleaded guilty to bombarding his former partner with a string of threatening text messages and phone calls between 13 June and 21 June.
However, he has since failed to appear in court for sentencing and police have issued a warrant for his arrest.
Police said Bond has connections to East and West Sussex, as well as Poole, Ferndown, Bournemouth, Weymouth and Wimbourne in Dorset, Salisbury in Wiltshire and Ringwood in Hampshire.
If you see him or know where he could be, please report it online or call 101 – or 999 in an emergency – quoting serial 1285 of 13/06.
Alternatively, you can visit the Crimestoppers website or contact the independent charity anonymously on 0800 555 111.