Keen horse stuck in bottom of Becher's Brook (6)
I believe the answer is:
shrill
'keen' is the definition.
(I've seen this before)
'horse stuck in bottom of becher's brook' is the wordplay.
'horse' becomes 'h' ('H' can be a synonym of 'horse').
'stuck in' indicates putting letters inside.
'bottom of' indicates one should take the final letters.
'brook' becomes 'rill' (I've seen this before).
The final letter of 'bechers' is 's'.
's'+'rill'='srill'
'h' placed within 'srill' is 'SHRILL'.
(Other definitions for shrill that I've seen before include "High and piercing" , "(Of a cry) piercing" , "Of voice, highl-pitched and loud" , "High pitched" , "Of sound, piercing and high-pitched" .)