Good boys head off at 1 PM (9)

I believe the answer is:

gladstone

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'pm' is the definition.
(Victorian UK prime minister William Gladstone)

'good boys head off at 1' is the wordplay.
'good boys' becomes 'glads' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'head off' means to remove the first letter.
'g' becomes 'one' (synonyms).
'at' with its initial letter removed is 't'.
'glads'+'t'+'one'='GLADSTONE'

Can you help me to learn more?

(Other definitions for gladstone that I've seen before include "5,27 [PRIME MINISTER]" , "Victorian GOM" , "Old English P.M. or a doctor's bag" , "C. nineteenth Liberal prime minister" , "Former English PM or kind of bag" .)

I've seen this clue in The Daily Express.

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