King drinking the French gin cocktail is at rest (8)
I believe the answer is:
relaxing
'at rest' is the definition.
(someone at rest is relaxing)
'king drinking the french gin cocktail' is the wordplay.
'king' becomes 'rex' ('king' in Latin).
'drinking' means one lot of letters goes inside another (inserted letters are consumed or drunk).
'the french' becomes 'la' ('the' in French).
'cocktail' indicates an anagram.
'rex' enclosing 'la' is 'relax'.
'gin' anagrammed gives 'ing'.
'relax'+'ing'='RELAXING'
'is' is the link.
(Other definitions for relaxing that I've seen before include "Taking it easy" , "Resting" , "At ease" , "Calming" , "Easeful" .)