Recklessly bid a lot for popular paper (7)
I believe the answer is:
tabloid
'popular paper' is the definition.
(as opposed to broadsheets)
'recklessly bid a lot' is the wordplay.
'recklessly' is an anagram indicator (I've seen this in other clues).
'bid'+'a'+'lot'='bidalot'
'bidalot' anagrammed gives 'TABLOID'.
'for' acts as a link.
(Other definitions for tabloid that I've seen before include "Popular newspaper size" , "Newspaper with half-size pages" , "Cheap newspaper" , "Small-size newspaper" , "Smaller-sized newspaper" .)