Bill with hat stuffed with old paper (7)
I believe the answer is:
tabloid
'paper' is the definition.
(type of newspaper)
'bill with hat stuffed with old' is the wordplay.
'bill' becomes 'tab' (tab is a kind of bill).
'with' means one lot of letters go next to another.
'hat' becomes 'lid' (synonyms).
'stuffed with' means one lot of letters goes inside another (some letters get stuffed inside).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'lid' going around 'o' is 'loid'.
'tab'+'loid'='TABLOID'
(Other definitions for tabloid that I've seen before include "Small-format newspaper" , "A bit old (anag)" , "Popular newspaper size" , "daily, perhaps" , "Populist newspaper" .)