Almost having taken head off, order dismissal (5,4)
I believe the answer is:
early bath
'dismissal' is the definition.
(early bath can mean an early dismissal)
'almost having taken head off order' is the wordplay.
'almost' becomes 'nearly' (synonyms).
'having taken head off' means to remove the first letter.
'order' becomes 'bath' (Order of the Bath, military order founded 1725).
'nearly' with its first letter removed is 'early'.
'early'+'bath'='EARLY BATH'
I've seen this clue in The Guardian.
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