Nevertheless one may be thought really to exist (4)
I believe the answer is:
yeti
'be thought really to exist' is the definition.
I can't judge whether this definition defines the answer.
'nevertheless one' is the wordplay.
'nevertheless' becomes 'yet' (I've seen this before).
'one' becomes 'i' (Roman numeral).
'yet'+'i'='YETI'
'may' is the link.
Can you help me to learn more?
(Other definitions for yeti that I've seen before include "Bigfoot" , "Himalayan wild man" , "It probably doesn't exist" , "creature awaiting discovery?" , "... and creature supposedly there" .)