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' is an insertion indicator (bag can mean secures or steals).
'queen' becomes 'ER' (short for Elizabeth Regina ie Queen Elizabeth).
'the largest share' becomes 'most' (I am not sure about this - if you are sure you should believe this answer much more).
'er'+'most'='ermost'
'that' placed 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" .)