All the best gold rings perish (5)
I believe the answer is:
adieu
'all the best' is the definition.
(both might be used when saying farewell)
'gold rings perish' is the wordplay.
'gold' becomes 'Au' (Au is the chemical symbol for gold).
'rings' indicates putting letters inside (some letters are ringed or contained by others).
'perish' becomes 'die' (synonyms).
'au' going around 'die' is 'ADIEU'.
(Other definitions for adieu that I've seen before include "I'm going" , "Auf wiedersehen" , "Farewell, adios" , "Au revoir (to a kind friend?)" , "12 Down" .)