Descent of eagle flying outside home (7)
I believe the answer is:
lineage
'descent' is the definition.
('lineage' can be a synonym of 'descent')
'eagle flying outside home' is the wordplay.
'flying' indicates anagramming the letters.
'outside' means one lot of letters goes inside another.
'home' becomes 'in' ('he's home' can mean 'he's in').
'eagle' is an anagram of 'leage'.
'leage' going around 'in' is 'LINEAGE'.
'of' is the link.
(Other definitions for lineage that I've seen before include "Descent (from an ancestor)" , "Ancestral line as seen in eagle" , "The strain" , "Genealogy" , "Old family members" .)