Show one's years in a sign of exhaustion (7)
I believe the answer is:
pageant
'show' is the definition.
(a show or display)
'one's years in a sign of exhaustion' is the wordplay.
'one's years' becomes 'age'.
'in' is an insertion indicator.
'a sign of exhaustion' becomes 'pant' (someone exhausted might pant).
'age' put inside 'pant' is 'PAGEANT'.
(Other definitions for pageant that I've seen before include "Rich parade" , "Colourful display or parade" , "Splendid procession, parade" , "Neat gap for colourful spectacle" , "entertaining spectacle" .)