Methedrine with gin mixed may be a driving offence (8)
I believe the answer is:
speeding
'a driving offence' is the definition.
(I've seen this before)
'methedrine with gin mixed' is the wordplay.
'methedrine' becomes 'speed' (synonyms).
'with' is a charade indicator (letters next to each other).
'mixed' indicates an anagram.
'gin' anagrammed gives 'ing'.
'speed'+'ing'='SPEEDING'
'may be' acts as a link.
(Other definitions for speeding that I've seen before include "Travelling at an illegal rate" , "Travelling too fast" , "Travelling rapidly" , "Moving very fast" , "Driving too fast" .)