Element of bitterness leading to one having hesitation (7)
I believe the answer is:
gallium
'element' is the definition.
(gallium is a kind of element)
'bitterness leading to one having hesitation' is the wordplay.
'bitterness' becomes 'gall' ('gall' can be a synonym of 'bitterness').
'leading to' is a charade indicator (letters next to each other) (some letters go before or lead others).
'one' becomes 'i' (Roman numeral).
'having' is a charade indicator (letters next to each other).
'hesitation' becomes 'um'.
'gall'+'i'+'um'='GALLIUM'
'of' is the link.
(Other definitions for gallium that I've seen before include "soft one" , "Metallic element" .)