Being old not right in secret organisation (9)
I believe the answer is:
existence
'being' is the definition.
('existence' can be a synonym of 'being')
'old not right in secret organisation' is the wordplay.
'old' becomes 'ex'.
'not' indicates named letters should be taken away.
'right' becomes 'r' (common abbreviation).
'organisation' is an anagram indicator.
'in'+'secret'='insecret'
'insecret' with 'r' removed is 'insecet'.
'insecet' is an anagram of 'istence'.
'ex'+'istence'='EXISTENCE'
(Other definitions for existence that I've seen before include "A way of living" , "The business of being" , "State of being" , "survival" , "Way of life" .)