Show how old one is in a gasp (7)
I believe the answer is:
pageant
'show' is the definition.
(a show or display)
'how old one is in a gasp' is the wordplay.
'how old one is' becomes 'age'.
'in' indicates putting letters inside.
'a gasp' becomes 'pant' (synonyms).
'age' put into 'pant' is 'PAGEANT'.
(Other definitions for pageant that I've seen before include "Splendid procession, parade" , "Elaborate procession on historical theme" , "Costumed procession" , "Parade with tableaux" , "Series of tableaux etc" .)