Paper a bit “old”, in need of redesign (7)
I believe the answer is:
tabloid
'paper' is the definition.
(type of newspaper)
'a bit old in need of redesign' is the wordplay.
'in need of redesign' indicates an anagram.
'a'+'bit'+'old'='abitold'
'abitold' is an anagram of 'TABLOID'.
(Other definitions for tabloid that I've seen before include "Newspaper with smaller pages and popular content" , "Ad lib to get lowbrow newspaper" , "Small-sized newspaper" , "A bit old (anag)" , "Cheap newspaper" .)