Correctional centre in Hampshire media lambasts (8)
I believe the answer is:
remedial
'correctional' is the definition.
'centre in hampshire media lambasts' is the wordplay.
'centre in' indicates the answer is hidden within the clue (the answer is hidden in the middle of the clue).
'REMEDIAL' is hidden in the letters of 'hampshire media lambasts'.
(Other definitions for remedial that I've seen before include "Putting things right" , "'Therapeutic, healing (8)'" , "Corrective" , "Providing a cure or treatment for illness or deficiency" , "for the lower classes" .)