Automatic control which bags queen the largest share (10)
I believe the answer is:
thermostat
'automatic control' is the definition.
'thermostat' can be an answer for 'control' (thermostat is a kind of control). I am not certain of the 'automatic' bit.
'which bags queen the largest share' is the wordplay.
'which' becomes 'that' ('that' and 'which' are often synonymous).
'bags' indicates putting letters inside (bag can mean secures or steals).
'queen' becomes 'ER' (abbreviation for Elizabeth Regina).
'the largest share' becomes 'most' (I can't justify this - if you can you should give a lot more credence to this answer).
'er'+'most'='ermost'
'that' going around 'ermost' is 'THERMOSTAT'.
Can you help me to learn more?
(Other definitions for thermostat that I've seen before include "Temperature regulator" , "Temperature controller" , "Heating device" , "Form of control" .)