Crime, trashing first lift (5)
I believe the answer is:
theft
'crime' is the definition.
(theft is a kind of crime)
'trashing first lift' is the wordplay.
'trashing first' becomes 't' (1st letter of 'trashing').
'lift' becomes 'heft' (hefting is a kind of lifting).
't'+'heft'='THEFT'
(Other definitions for theft that I've seen before include "Robbery" , "crime incident" , "Taking of another's property" , "Pilferage" , "Dishonest appropriation" .)