Posh private among soldiers — a considerable number! (7)
I believe the answer is:
umpteen
'a considerable number' is the definition.
(I've seen this in another clue)
'posh private among soldiers' is the wordplay.
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-U).
'private' becomes 'pte'.
'among' is an insertion indicator (inserted letters are placed among others).
'soldiers' becomes 'men' (men can mean a group of soldiers).
'pte' put into 'men' is 'mpteen'.
'u'+'mpteen'='UMPTEEN'
(Other definitions for umpteen that I've seen before include "An uncountable number" , "Unspecified large number" , "Lots of things on pet menu" , "Quite a lot of (sl)" , "Guarded" .)