Extremely savvy fellow backed church council (5)
I believe the answer is:
synod
'church council' is the definition.
(I've seen this before)
'extremely savvy fellow backed' is the wordplay.
'extremely' means to remove the middle letters.
'fellow' becomes 'don' (I've seen this before).
'backed' says the letters should be written in reverse.
'savvy' with its centre taken out is 'sy'.
'don' in reverse letter order is 'nod'.
'sy'+'nod'='SYNOD'
(Other definitions for synod that I've seen before include "Church assembly" , "council meeting" , "Ecclesiastic council" , "group of clergymen" , "Ecumenical council" .)