Count, after support, is on the wagon (8)
I believe the answer is:
teetotal
'on the wagon' is the definition.
(thesaurus)
'count after support' is the wordplay.
'count' becomes 'total' (totaling is a kind of counting**).
'after' is a charade indicator (letters next to each other).
'support' becomes 'tee' (I've seen this before).
'total' put after 'tee' is 'TEETOTAL'.
'is' is the link.
(Other definitions for teetotal that I've seen before include "On the wagon" , "Completely dry" , "Abstinent from alcohol" , "Abstaining completely from alcohol" , "Never touching 13" .)