Caution, twenty-four hours after promotion? Rather! (8)
I believe the answer is:
admonish
'caution' is the definition.
(synonyms)
'twenty-four hours after promotion? rather' is the wordplay.
'twenty-four hours' becomes 'Mon' (Monday).
'after' says to put letters next to each other.
'promotion?' becomes 'ad' (short for advert).
'rather' becomes 'ish' (I can't explain this - if you can you should give a lot more credence to this answer).
'mon' after 'ad' is 'admon'.
'admon'+'ish'='ADMONISH'
Can you help me to learn more?
(Other definitions for admonish that I've seen before include "Chide, reprove" , "Reprove, warn" , "Caution - reprimand" , "Tell off" , "Rebuke, tick off" .)