Encourage chef to evict loud queen (5)
I believe the answer is:
cheer
'encourage' is the definition.
(I know that cheer is a kind of encourage)
'chef to evict loud queen' is the wordplay.
'to evict' indicates named letters should be taken away.
'loud' becomes 'f' (short for forte - 'loud' in music).
'queen' becomes 'ER' (abbreviation for Elizabeth Regina).
'chef' with 'f' removed is 'che'.
'che'+'er'='CHEER'
(Other definitions for cheer that I've seen before include "Buck up" , "party refreshment?" , "Encourage - applaud" , "one in three, perhaps" , "pair of hips can get me going!" .)