Middle name put first in place for telephone operators (4,6)
I believe the answer is:
call centre
'place for telephone operators' is the definition.
'middle name put first' is the wordplay.
'middle' becomes 'centre' ('centre' can be a synonym of 'middle').
'name' becomes 'call' (a name is a call-sign).
'put first' is a charade indicator (letters next to each other).
'centre' after 'call' is 'CALL CENTRE'.
'in' is the link.
(Other definitions for call centre that I've seen before include "Office with many phones" , "Telephone answering office" , "Phone here for help" , "Workplace" .)