Answer arrived about Donne's case in scholarly life (7)
I believe the answer is:
'scholarly life' is the definition.
'answer arrived about donne's case' is the wordplay.
'answer' becomes 'a' (abbreviation eg in Q and A).
'arrived' becomes 'came' (come can mean to appear or arrive).
'about' means one lot of letters goes inside another.
'case' suggests removing the centre.
'donne' with its middle removed is 'de'.
'came' placed around 'de' is 'cademe'.
'in' acts as a link.
(Other definitions for academe that I've seen before include "World of scholarship" , "University environment" , "The world of education" , "The world of learning" , "learned environment" .)