Show decline in gasp for breath (7)
I believe the answer is:
pageant
'show' is the definition.
(a show or display)
'decline in gasp for breath' is the wordplay.
'decline' becomes 'age' (get older).
'in' means one lot of letters goes inside another.
'gasp for breath' becomes 'pant' (I've seen this before).
'age' put inside 'pant' is 'PAGEANT'.
(Other definitions for pageant that I've seen before include "Neat gap for colourful spectacle" , "Dramatic performance" , "Costumed procession" , "Spectacular parade" , "entertaining spectacle" .)