Chewing a mint as they demonstrate staying power (7)
I believe the answer is:
stamina
'staying power' is the definition.
(synonyms)
'chewing a mint as' is the wordplay.
'chewing' indicates an anagram.
'a'+'mint'+'as'='amintas'
'amintas' anagrammed gives 'STAMINA'.
'they demonstrate' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for stamina that I've seen before include "Sustained energy" , "bottom" , "capability to keep going" , "having more to call on" , "The ability to sustain prolonged physical or mental effort" .)