Discourage Mike: Daisy upset outside (6)
I believe the answer is:
dismay
'discourage' is the definition.
(dismaying is a kind of discouraging)
'mike daisy upset outside' is the wordplay.
'mike' becomes 'M' (phonetic alphabet: alpha, bravo, charlie etc.).
'upset' is an anagram indicator.
'outside' means one lot of letters goes inside another.
'daisy' with letters rearranged gives 'disay'.
'm' going inside 'disay' is 'DISMAY'.
(Other definitions for dismay that I've seen before include "trouble" , "Appal" , "Feeling of despair in the face of obstacles" , "Consternation, discouragement" , "Alarm, distress" .)