Beseech to take in a living creature (5)
I believe the answer is:
being
'a living creature' is the definition.
(I've seen this before)
'beseech to take in' is the wordplay.
'beseech' becomes 'beg' (I've seen this before).
'to take' is an insertion indicator.
'beg' enclosing 'in' is 'BEING'.
(Other definitions for being that I've seen before include "A matter of 9 in the play" , "Human, perhaps" , "Living thing" , "See 9" , "A living creature" .)