Search disposing of Queen’s concern (4)
I believe the answer is:
fret
'concern' is the definition.
(thesaurus)
'search disposing of queen's' is the wordplay.
'search' becomes 'ferret' (ferret can mean to search around for something).
'disposing of' indicates named letters should be taken away.
'queen' becomes 'ER' (abbreviation for Elizabeth Regina).
'ferret' with 'er' taken out is 'FRET'.
(Other definitions for fret that I've seen before include "Wear; guitar ridge" , "Worry about doing woodwork?" , "worry its way through?" , "Distress oneself" , "Worry; wet mist" .)