Private and fancy aren't in line (8)
I believe the answer is:
internal
'private' is the definition.
(thesaurus)
'fancy aren't in line' is the wordplay.
'fancy' indicates an anagram.
'line' becomes 'l'.
'arent'+'in'='arentin'
'arentin' is an anagram of 'interna'.
'interna'+'l'='INTERNAL'
'and' is the link.
(Other definitions for internal that I've seen before include "In-house - private" , "Located inside" , "Located inward" , "Inside the body" , "Within the body" .)