Traced new and old decorative style (3,4)
I believe the answer is:
art deco
'decorative style' is the definition.
(I've seen this before)
'traced new and old' is the wordplay.
'new' indicates an anagram.
'and' says to put letters next to each other.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'traced' with letters rearranged gives 'artdec'.
'artdec'+'o'='ART DECO'
(Other definitions for art deco that I've seen before include "1920s and 1930s ornamental style" , "1920s and 30s style of art and architecture" , "Nineteen twenty's and thirties style" , "modern style" , "Style characterised by bold geometric shapes" .)