Rather agitated, holding live element (4,5)
I believe the answer is:
rare earth
'element' is the definition.
(rare-earth element is a kind of element)
'rather agitated holding live' is the wordplay.
'agitated' is an anagram indicator.
'holding' is an insertion indicator.
'live' becomes 'are' (both can mean exist).
'rather' anagrammed gives 'rearth'.
'rearth' going around 'are' is 'RARE-EARTH'.
(Other definitions for rare earth that I've seen before include "element such as promethium" , "metallic element" , "Metal" , "One of a group of 15 hard to distinguish elements - at her rear (anag)" , "Oxide" .)