Calm down idiot before second half of speech (7)
I believe the answer is:
assuage
'calm down' is the definition.
(assuage can mean to calm down or relieve)
'idiot before second half of speech' is the wordplay.
'idiot before' becomes 'ass' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'second half of' means to take half the letters (the back or second half of the word).
'speech' becomes 'language' (synonyms).
'language' with half the letters taken is 'uage'.
'ass'+'uage'='ASSUAGE'
(Other definitions for assuage that I've seen before include "9 across (anag)" , "Ease or relieve, say thirst" , "Provide physical or mental relief -- satisfy" , "moderate" , "Mitigate - allay" .)