Beggars once covering this crime (5)
I believe the answer is:
arson
'this crime' is the definition.
(I've seen this before)
'beggars once covering' is the wordplay.
'covering' indicates a hidden word.
'ARSON' is hidden in the letters of 'beggars once'.
(Other definitions for arson that I've seen before include "Malicious fire-lighting" , "It may get you in court" , "Criminal burning of property" , "A burning crime" , "Incendiarism" .)