Bizarre shared wish to get this appliance (10)
I believe the answer is:
dishwasher
'this appliance' is the definition.
(dishwasher is a kind of appliance)
'bizarre shared wish' is the wordplay.
'bizarre' is an anagram indicator.
'shared'+'wish'='sharedwish'
'sharedwish' is an anagram of 'DISHWASHER'.
'to get' acts as a link.
(Other definitions for dishwasher that I've seen before include "Appliance for cleaning plates, cutlery etc" , "cleaner" , "Kitchen machine" , "kitchen helper" , "Kitchen item" .)