European educational foundation concealing old mistake (5)
I believe the answer is:
error
'mistake' is the definition.
('error' can be a synonym of 'mistake')
'european educational foundation concealing old' is the wordplay.
'european' becomes 'e' (abbreviation e.g. EU).
'educational foundation' becomes 'rrr' (the three R's: writing, reading, arithmetic).
'concealing' means one lot of letters goes inside another.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'rrr' enclosing 'o' is 'rror'.
'e'+'rror'='ERROR'
(Other definitions for error that I've seen before include "Trial and ___" , "wrong" , "Miscarriage of justice" , "Slip-up" , "Bug" .)