Wisely arch about how old one is (6)
I believe the answer is:
sagely
'wisely' is the definition.
(synonyms)
'arch about how old one is' is the wordplay.
'arch' becomes 'sly' (both can mean clever or sneaky).
'about' indicates putting letters inside.
'how old one is' becomes 'age'.
'sly' placed around 'age' is 'SAGELY'.
(Other definitions for sagely that I've seen before include "Wisely" , "As someone wise" , "In a wise manner" , "Like wise guy" , "with wisdom" .)