A great many put me out — active men, ultimately (7)
I believe the answer is:
umpteen
'a great many' is the definition.
'put me out active men ultimately' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'ultimately' says to take the final letters.
The final letters of 'active men' are 'en'.
'put'+'me'='putme'
'putme' anagrammed gives 'umpte'.
'umpte'+'en'='UMPTEEN'
(Other definitions for umpteen that I've seen before include "Informally, very many" , "An uncountable number" , "Unspecified large number" , "Lots of things on pet menu" , "Plentiful" .)