Email, when sloshed at the same time (9)
I believe the answer is:
meanwhile
'at the same time' is the definition.
(synonyms)
'email when sloshed' is the wordplay.
'sloshed' indicates an anagram.
'email'+'when'='emailwhen'
'emailwhen' with letters rearranged gives 'MEANWHILE'.
(Other definitions for meanwhile that I've seen before include "In the intervening time" , "For the moment" , "In the interim" , "simultaneously" , "in intervening period" .)