Others managed these at first, including a posh eating-place (10)
I believe the answer is:
restaurant
'eating-place' is the definition.
I can't tell whether this definition defines the answer.
'others managed these at first including a posh' is the wordplay.
'others' becomes 'rest' (eg the rest of a group).
'managed these at first' becomes 'rant' (I can't justify this - if you can you should give a lot more credence to this answer).
'including' is an insertion indicator.
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-U).
'rest'+'rant'='restrant'
'a'+'u'='au'
'restrant' enclosing 'au' is 'RESTAURANT'.
Can you help me to learn more?
(Other definitions for restaurant that I've seen before include "Eating place" , "Eatery" , "table here?" .)