One of the first people entered, ignoring me (4)
I believe the answer is:
cain
'one of the first people' is the definition.
(son of Adam and Eve)
'entered ignoring me' is the wordplay.
'entered' becomes 'came in' (to come in is to enter).
'ignoring' is a deletion indicator.
'camein' with 'me' taken out is 'CAIN'.
(Other definitions for cain that I've seen before include "Eve's firstborn" , "Adam's son" , "Abel's brother" , "Eldest son of Adam, Eve" , "The first known murderer" .)