Unimportant false alarm I emit (10)
I believe the answer is:
immaterial
'unimportant' is the definition.
(thesaurus)
'false alarm i emit' is the wordplay.
'false' indicates an anagram.
'alarm'+'i'+'emit'='alarmiemit'
'alarmiemit' with letters rearranged gives 'IMMATERIAL'.
(Other definitions for immaterial that I've seen before include "unimportant" , "of no importance" , "Irrelevant" .)