She had an eagle, almost, going out (6)
I believe the answer is:
angela
'she' is the definition.
(I've seen this before)
'an eagle almost going out' is the wordplay.
'almost' means to remove the first letter.
'going out' is an anagram indicator (out can mean wrong or inaccurate).
'eagle' with its first letter removed is 'agle'.
'agle' is an anagram of 'gela'.
'an'+'gela'='ANGELA'
'had' is the link.
(Other definitions for angela that I've seen before include "------ Gheorghiu, diva" , ". . . Lansbury (actress)" , "-- Merkel, German Chancellor" , "- Carter, English writer" , "Frau Merkel" .)