Write on science and the study of Crime and Punishment (8)
I believe the answer is:
penology
'the study of crime and punishment' is the definition.
(I've seen this before)
'write on science' is the wordplay.
'write' becomes 'pen' ('pen' can be a synonym of 'write').
'on' means one lot of letters go next to another.
'science' becomes 'ology' (I've seen this before).
'pen'+'ology'='PENOLOGY'
'and' acts as a link.
(Other definitions for penology that I've seen before include "Study of crime and punishment" , "The scientific study of crime, prison etc" .)