Record is number one a short time (4)
I believe the answer is:
memo
'record' is the definition.
(memo is a kind of record)
'number one a short time' is the wordplay.
'number one' becomes 'me'.
'a short time' becomes 'mo' (as in 'just a mo').
'me'+'mo'='MEMO'
'is' acts as a link.
(Other definitions for memo that I've seen before include "A brief record of events" , "Brief note, usually between co-workers" , "Office note" , "- Currie, Br. politician" , "Note written as a reminder" .)