Peer puts nothing in grain store (5)
I believe the answer is:
baron
'peer' is the definition.
(baron is a kind of peer)
'nothing in grain store' is the wordplay.
'nothing' becomes 'O' (looks like zero - 0).
'in' means one lot of letters goes inside another.
'grain store' becomes 'barn' (I am not sure about this - if you are sure you should believe this answer much more).
'o' inserted into 'barn' is 'BARON'.
'puts' acts as a link.
Can you help me to learn more?
(Other definitions for baron that I've seen before include "Born a (anagram) - powerful man of business" , "A lord; sounds like childless" , "A born nobleman" , "Title of rank" , "captain of industry" .)