Private taxi almost back in one minute, making turn (7)
I believe the answer is:
minicab
'private taxi' is the definition.
(a minicab is a taxi booked in advance)
'almost back in one minute making turn' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'one' becomes 'i' (Roman numeral).
'minute' becomes 'm' (abbreviation).
'making turn' says the letters should be written in reverse (letters turn around).
'back' with its last letter removed is 'bac'.
'bac'+'in'+'i'+'m'='bacinim'
'bacinim' written backwards gives 'MINICAB'.
(Other definitions for minicab that I've seen before include "Metered vehicle for hire" , "Type of car hire" , "Car used as taxi" , "transport" , "Hired vehicle" .)