Mind - one might have to be hung out to dry after this, as it's part of the conditioning
I believe the answer is:
brainwashing
'the conditioning' is the definition.
(thesaurus)
'mind one might have' is the wordplay.
'mind' becomes 'brain' ('brain' can be a synonym of 'mind').
'one might have' becomes 'washing' (I can't justify this - if you can you should give a lot more credence to this answer).
'brain'+'washing'='BRAINWASHING'
'to be hung out to dry after this as it's part of' is the 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 brainwashing that I've seen before include "Changing mind" , "Totally indoctrinating" , "Systematic indoctrination" .)