Selfish being last to come and first to leave (6)
I believe the answer is:
egoist
'selfish being' is the definition.
'last to come and first to leave' is the wordplay.
'last to' suggests the final letters.
'and' is a charade indicator (letters next to each other).
'first' becomes 'ist' (**).
'to' says to put letters next to each other (I've seen this in other clues).
'leave' becomes 'go'.
The final letter of 'come' is 'e'.
'ist' after 'go' is 'goist'.
'e' put next to 'goist' is 'EGOIST'.
(Other definitions for egoist that I've seen before include "A self-obsessed or very vain person" , "Self-seeker" , "self-seeking type" , "Narcissist" , "It goes with self-centred man" .)