Vouch for the account many tried falsely (8)
I believe the answer is:
accredit
'vouch for' is the definition.
(thesaurus)
'account many tried falsely' is the wordplay.
'account' becomes 'ac' (abbreviation).
'many' becomes 'c' (C is the Roman numeral for 100).
'falsely' is an anagram indicator.
'tried' is an anagram of 'redit'.
'ac'+'c'+'redit'='ACCREDIT'
'the' is the link.
(Other definitions for accredit that I've seen before include "Cat cried (anag.)" , "Accept as true" , "Authorize" , "Give official sanction to (a diplomat)" , "Officially recognise" .)