After a trio performs, coming on to make a speech (7)
I believe the answer is:
oration
'a speech' is the definition.
(oration is a kind of speech)
'after a trio performs coming on to' is the wordplay.
'after' becomes 'on' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'performs' is an anagram indicator.
'coming on to' means one lot of letters go next to another.
'a'+'trio'='atrio'
'atrio' with letters rearranged gives 'orati'.
'on' after 'orati' is 'ORATION'.
'make' acts as a link.
Can you help me to learn more?
(Other definitions for oration that I've seen before include "An eloquent speech" , "Address" , "words" , "Type 16 [OF SPEECH]" , "Power of speech" .)