Given restrictions, a sports car's overtaken a mile back (3,6)

'given restrictions' is the definition.

'a sports car's overtaken a mile back' is the wordplay.
I cannot quite understand how this works, but
'a' is present in the answer.
'car's' could be 'ts' and 'ts' is present in the answer.
an anagram of 'mile' is 'elim' which is within the answer.
The remaining letters 'gi' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...