Writer given second reminder (4)
I believe the answer is:
memo
'reminder' is the definition.
(I've seen this in another clue)
'writer given second' is the wordplay.
'writer' becomes 'me' (the person who wrote the clues).
'given' says to put letters next to each other.
'second' becomes 'mo' (both are short periods of time).
'me'+'mo'='MEMO'
(Other definitions for memo that I've seen before include "A brief record of events" , "Note written as a reminder" , "Reminder (abbr)" , "A little something to be remembered" , "Written business message, in short" .)