Improve a lime concoction so to speak (10)
I believe the answer is:
ameliorate
'improve' is the definition.
('ameliorate' can be a synonym of 'improve')
'a lime concoction so to speak' is the wordplay.
'concoction' indicates an anagram.
'so to speak' becomes 'orate' (I can't justify this - if you can you should give a lot more credence to this answer).
'lime' is an anagram of 'meli'.
'a'+'meli'+'orate'='AMELIORATE'
(Other definitions for ameliorate that I've seen before include "Make (something) better" , "Make (a bad thing) better" , "seen to improve" , "Become better" .)