Assistants covering up spook's initial digressions (6)
I believe the answer is:
asides
'digressions' is the definition.
('aside' can be a synonym of 'digression')
'assistants covering up spook's initial' is the wordplay.
'assistants' becomes 'aides' (aide is a kind of assistant).
'covering up' indicates putting letters inside.
'initial' says to take the initial letters.
The initial letter of 'spooks' is 's'.
'aides' going around 's' is 'ASIDES'.
(Other definitions for asides that I've seen before include "Words spoken on stage" , "They're not heard by everybody" , "Words spoken so that certain people won't hear" , "Remarks not for overhearing" , "Stage whisper" .)