Lessens the chance of upsetting a beast (6)
I believe the answer is:
abates
'lessens the chance' is the definition.
'abates' can be an answer for 'lessens' (abating is a kind of lessening). I am not certain of the 'the chance' bit.
'upsetting a beast' is the wordplay.
'upsetting' is an anagram indicator.
'a'+'beast'='abeast'
'abeast' anagrammed gives 'ABATES'.
'of' acts as a link.
Can you help me to learn more?
(Other definitions for abates that I've seen before include "Becomes less severe or strong" , "has a fall" , "Goes down like storm" , "Calms down a" , "Grows less intense" .)