Arriving with nothing, first to greet worker, conceited (8)
I believe the answer is:
arrogant
'conceited' is the definition.
(I've seen this before)
'arriving with nothing first to greet worker' is the wordplay.
'arriving' becomes 'arr' (abbreviation used in transport).
'with' says to put letters next to each other.
'nothing' becomes 'O' (O resembles 0).
'first to' suggests taking the first letters.
'worker' becomes 'ant' (worker is a type of ant).
The first letter of 'greet' is 'g'.
'arr'+'o'+'g'+'ant'='ARROGANT'
(Other definitions for arrogant that I've seen before include "Overbearing; conceited" , "Proud and overbearing, feeling superior" , "Disdainful" , "Overweening" , "Public speaker" .)