Second, then less specific date reference (5)
I believe the answer is:
month
'second then less specific date reference' is the definition.
'month' can be an answer for 'second' (thesaurus). I am unsure of the 'then less specific date reference' bit.
'second then less specific date reference' is the wordplay.
'second' becomes 'mo' (both are short periods of time).
'then less specific date reference' becomes 'nth' (I can't explain this - if you can you should give a lot more credence to this answer).
'mo'+'nth'='MONTH'
Can you help me to learn more?
(Other definitions for month that I've seen before include "See 10" , "May, perhaps" , "Four-week period" , "One of 12 divisions" , "Eg, April" .)