Second husband in sophisticated institution (6)
I believe the answer is:
school
'institution' is the definition.
(school is a kind of institution)
'second husband in sophisticated' is the wordplay.
'second' becomes 's' (common abbreviation).
'husband' becomes 'h'.
'in' is an insertion indicator.
'sophisticated' becomes 'cool'.
'h' going inside 'cool' is 'chool'.
's'+'chool'='SCHOOL'
(Other definitions for school that I've seen before include "Where one teaches" , "Teach; group of fish" , "Group of sea creatures" , "a lot of swimmers" , "Teaching establishment" .)