A set of books taking in extremely gullible representative (5)
I believe the answer is:
agent
'representative' is the definition.
(agent is a kind of representative)
'a set of books taking in extremely gullible' is the wordplay.
'a set of books' becomes 'ant'.
'taking in' indicates putting letters inside.
'extremely' means to remove the middle letters.
'gullible' with its middle removed is 'ge'.
'ant' placed around 'ge' is 'AGENT'.
(Other definitions for agent that I've seen before include "Sales rep" , "One does business on behalf of another" , "Substance that exerts some force or effect" , "Performer's manager" , "Spy; service provider" .)