Isolated group is wretched clan embraced by First Lady (7)
I believe the answer is:
enclave
'isolated group' is the definition.
(I've seen this before)
'wretched clan embraced by first lady' is the wordplay.
'wretched' is an anagram indicator.
'embraced by' indicates putting letters inside.
'first lady' becomes 'eve' (Biblical first woman).
'clan' is an anagram of 'ncla'.
'ncla' put within 'eve' is 'ENCLAVE'.
'is' is the link.
(Other definitions for enclave that I've seen before include "Group ethnically different from those around it" , "Surrounded area of a different ethnicity" , "pocket" , "Territory enclosed within another one" , "Region wholly within another" .)