Eccentric lady buying Independent newspaper (5)
I believe the answer is:
daily
'newspaper' is the definition.
(daily is a kind of newspaper)
'eccentric lady buying independent' is the wordplay.
'eccentric' indicates anagramming the letters.
'buying' indicates putting letters inside (inserted letters are acquired or 'bought').
'independent' becomes 'i'.
'lady' with letters rearranged gives 'daly'.
'daly' placed around 'i' is 'DAILY'.
(Other definitions for daily that I've seen before include "paper, of a sort" , "regularly" , "A rag, perhaps" , "Quotidian" , "Newspaper; cleaner" .)