Turn up, initially taking chance on me (4)
I believe the answer is:
come
'turn up' is the definition.
(both can mean to arrive)
'initially taking chance on me' is the wordplay.
'initially taking' says to take the initial letters.
The first letters of 'chance on' is 'co'.
'co'+'me'='COME'
(Other definitions for come that I've seen before include "' - - fly with me'" , "Arrive" , "Make a forceful impression" , "Draw near" , "See 13 across" .)