Still independent, being of elusive nature (4)
I believe the answer is:
yeti
'being of elusive nature' is the definition.
(yetis are either non-existent or very elusive)
'still independent' is the wordplay.
'still' becomes 'yet' (synonyms).
'independent' becomes 'i'.
'yet'+'i'='YETI'
(Other definitions for yeti that I've seen before include "It's fantastic being" , "Mythical Tibetan beast" , "Mythical humanoid" , "Creature of disputed existence" , "Himalayan mystery" .)