Breathe heavily after somersault that's frivolous (8)
I believe the answer is:
flippant
'frivolous' is the definition.
(similar in meaning)
'breathe heavily after somersault' is the wordplay.
'breathe heavily' becomes 'pant' (I've seen this before).
'after' is a charade indicator (letters next to each other).
'somersault' becomes 'flip' (synonyms).
'pant' put after 'flip' is 'FLIPPANT'.
'that's' is the link.
(Other definitions for flippant that I've seen before include "Off-hand, frivolous in speech" , "anything but serious" , "Light-hearted" , "Cheeky" , "Not showing proper seriousness, disrespectful" .)