Prompt to secure a rest (9)
I believe the answer is:
remainder
'rest' is the definition.
(I know that rest can be written as remainder)
'prompt to secure a' is the wordplay.
'prompt' becomes 'reminder' (I've seen this in another clue).
'to secure' indicates putting letters inside (inserted letters are secured inside).
'reminder' enclosing 'a' is 'REMAINDER'.
(Other definitions for remainder that I've seen before include "Dispose of unsold books cheaply" , "Scrap" , "set of unsold books" , "butt" , "It's left over after division" .)