Joy, it's time to get into breathing out, having dropped an aitch! (10)
I believe the answer is:
exaltation
'joy' is the definition.
(thesaurus)
'time to get into breathing out having dropped an aitch' is the wordplay.
'time' becomes 't' (abbreviation).
'to get into' is an insertion indicator.
'breathing out' becomes 'exhalation' (to exhale is to breathe out).
'having dropped' indicates named letters should be taken away.
'an aitch' becomes 'H' (aitch is the name for the letter H).
'exhalation' with 'h' taken away is 'exalation'.
't' put into 'exalation' is 'EXALTATION'.
'it's' acts as a link.
(Other definitions for exaltation that I've seen before include "Extreme happiness" , "delight" , "Larks" .)