Going on to settle, following apprehension initially (5)
I believe the answer is:
afoot
'going on' is the definition.
(I've seen this in another clue)
'settle following apprehension initially' is the wordplay.
'settle' becomes 'foot' (in the sense of footing a bill).
'following' says to put letters next to each other.
'initially' says to take the initial letters.
The initial letter of 'apprehension' is 'a'.
'foot' after 'a' is 'AFOOT'.
'to' acts as a link.
(Other definitions for afoot that I've seen before include "In the pipeline" , "Making progress" , "Under way (like hunted game?)" , "Brewing" , "Happening" .)