Style worn by new Danish king (4)
I believe the answer is:
cnut
'danish king' is the definition.
(King Cnut, 10th- and 11th-century king)
'style worn by new' is the wordplay.
'style' becomes 'cut' (synonyms).
'worn by' indicates putting letters inside (I've seen this in other clues).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'cut' going around 'n' is 'CNUT'.
(Other definitions for cnut that I've seen before include "Old king of England" , "who demonstrated his limited powers?" , "King of Denmark, England and Norway" , "Ancient king" , "Danish king of England" .)