In extremis, secretary drops off church councils (6)
I believe the answer is:
synods
'church councils' is the definition.
(I've seen this in another clue)
'in extremis secretary drops off' is the wordplay.
'in extremis' says to hollow out the word (remove centre letters) (only the letters on the extremes are used).
'drops off' becomes 'nods' (I've seen this in another clue).
'secretary' with its centre taken out is 'sy'.
'sy'+'nods'='SYNODS'
(Other definitions for synods that I've seen before include "Councils of bishops" , "Council meetings of clergy to discuss policy" , "Council to discuss ecclesiastical business" , "Councils attended by clergy to discuss policy" , "Ecclesiastical councils" .)