Possibly border on a criminal act (6)
I believe the answer is:
mayhem
'criminal act' is the definition.
'mayhem' can be an answer for 'act' (mayhem is a kind of act). I am not sure about the 'criminal' bit.
'possibly border on a' is the wordplay.
'possibly' becomes 'my' (I can't explain this - if you can you should give a lot more credence to this answer).
'border' becomes 'hem' (I've seen this before).
'on' indicates putting letters inside (as in clothing 'on' a person).
'my'+'hem'='myhem'
'myhem' going around 'a' is 'MAYHEM'.
Can you help me to learn more?
(Other definitions for mayhem that I've seen before include "Chaos, violent disorder" , "wild state" , "Havoc - chaos" , "violence" , "Total chaos" .)