Strange rite involves adult being angry (5)
I believe the answer is:
irate
'angry' is the definition.
(irate can mean angry or annoyed)
'strange rite involves adult' is the wordplay.
'strange' is an anagram indicator.
'involves' is an insertion indicator.
'adult' becomes 'a' (abbreviation).
'rite' is an anagram of 'irte'.
'irte' enclosing 'a' is 'IRATE'.
'being' is the link.
(Other definitions for irate that I've seen before include "Angry - furious" , "Narked" , "Not happy" , "I tear away, being annoyed" , "Hacked off" .)