A lot of eastern men put out (7)
I believe the answer is:
umpteen
'a lot of' is the definition.
(I've seen this before)
'eastern men put out' is the wordplay.
'eastern' becomes 'e'.
'out' indicates an anagram (out can mean wrong or inaccurate).
'e'+'men'+'put'='emenput'
'emenput' with letters rearranged gives 'UMPTEEN'.
(Other definitions for umpteen that I've seen before include "Quite a lot of (sl)" , "Indefinitely many" , "Large but indefinite number" , "Uncountably many" , "Plentiful" .)