Alienate bishop leaving most agreeable mountain chain (8)
I believe the answer is:
estrange
'alienate' is the definition.
(synonyms)
'bishop leaving most agreeable mountain chain' is the wordplay.
'bishop' becomes 'b' (abbreviation used in chess).
'leaving' indicates named letters should be taken away.
'most agreeable' becomes 'best'.
'mountain chain' becomes 'range' (synonyms).
'best' with 'b' taken away is 'est'.
'est'+'range'='ESTRANGE'
(Other definitions for estrange that I've seen before include "Drive away" , "Become unfriendly towards sergeant" , "may break up" , "Make enemy of sergeant" , "Cause to be alienated" .)