Mediator flabbergasted with me: that's excessive! (10)
I believe the answer is:
immoderate
'excessive' is the definition.
(similar in meaning)
'mediator flabbergasted with me' is the wordplay.
'flabbergasted with' indicates anagramming the letters (I've seen this in other clues).
'mediator' mixed up with 'me' can make 'IMMODERATE'.
'that's' is the link.
(Other definitions for immoderate that I've seen before include "over the top" , "Excessive" , "Extravagant" , "Reckless" .)