Give up power and become less intense, keeping daughter in charge (8)
I believe the answer is:
abdicate
'give up power' is the definition.
(I've seen this before)
'become less intense keeping daughter in charge' is the wordplay.
'become less intense' becomes 'abate' (I've seen this before).
'keeping' means one lot of letters goes inside another.
'daughter' becomes 'd'.
'in charge' becomes 'ic'.
'd'+'ic'='dic'
'abate' going around 'dic' is 'ABDICATE'.
'and' is the link.
(Other definitions for abdicate that I've seen before include "Renounce position or power" , "surrender" , "Abandon" , "Give up a throne" , "Give up power" .)