Qualification of the First Lady accepted by everyone (1,5)
I believe the answer is:
a level
'qualification' is the definition.
(I know that A Level is a type of qualification)
'first lady accepted by everyone' is the wordplay.
'first lady' becomes 'eve' (first woman in the Bible).
'accepted by' means one lot of letters goes inside another (inserted letters are accepted).
'everyone' becomes 'all' (all people).
'eve' placed within 'all' is 'A-LEVEL'.
'of the' acts as a link.
(Other definitions for a level that I've seen before include "British education standard" , "Final exam for students at secondary school" , "'British school examination (1,5)'" , "Sixth-form exam" , "Advanced exam" .)