Student of wrongdoing caught China expert heading off across border (13)
I believe the answer is:
criminologist
'student of wrongdoing' is the definition.
(someone who studies crime)
'caught china expert heading off across border' is the wordplay.
'caught' becomes 'c' (cricket abbreviation).
'china expert' becomes 'Sinologist' (expert in China).
'heading off' means to remove the first letter.
'across' is an insertion indicator.
'border' becomes 'rim' (both can mean an edge).
'sinologist' with its first letter taken off is 'inologist'.
'c'+'inologist'='cinologist'
'cinologist' going around 'rim' is 'CRIMINOLOGIST'.
(Other definitions for criminologist that I've seen before include "One studying felons" , "Expert in breaking the law?" , "One studying law-breakers" , "Low-life expert" , "One who studies felons" .)