Third note, then second note (4)
I believe the answer is:
memo
'note' is the definition.
(memo is a kind of note)
'third note then second' is the wordplay.
'third note' becomes 'me' (as in do-re-mi).
'then' 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 "diplomatic communication?" , "In brief, a note of events" , "Reminder (abbr)" , "Short note or message" , "Written business message, in short" .)