Follow career after end of placement (5)
I believe the answer is:
trace
'follow' is the definition.
(I know that follow can be written as trace)
'career after end of placement' is the wordplay.
'career' becomes 'race' (career can mean to race around).
'after' is a charade indicator (letters next to each other).
'end of' indicates one should take the final letters.
The final letter of 'placement' is 't'.
'race' after 't' is 'TRACE'.
(Other definitions for trace that I've seen before include "Skimpy garment" , "Very small amount that can only just be detected" , "Element" , "part of harness" , "mark" .)