Err in detention? Get three deductions as a disincentive (9)
I believe the answer is:
deterrent
'a disincentive' is the definition.
(I've seen this before)
'err in detention?' is the wordplay.
'in' means one lot of letters goes inside another.
'detention?' becomes 'detent' (I can't justify this - if you can you should give a lot more credence to this answer).
'err' inserted inside 'detent' is 'DETERRENT'.
'get three deductions as' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for deterrent that I've seen before include "Eg, a nuclear weapon" , "It discourages someone from doing something" , "Something that puts people off" , "Something discouraging action" , "Something designed to be off-putting" .)