Second entry in assignment following study (11)
I believe the answer is:
readmission
'second entry' is the definition.
(entering or being admitted again)
'assignment following study' is the wordplay.
'assignment' becomes 'mission' (mission is a kind of assignment).
'following' means one lot of letters go next to another.
'study' becomes 'read' (synonyms).
'mission' put after 'read' is 'READMISSION'.
'in' acts as a link.
(Other definitions for readmission that I've seen before include "This gains one further acceptance" , "getting back in" , "Being allowed back in" , "entrance again" , "allowing visitors back in?" .)