Second daughter is up-to-date (3)
I believe the answer is:
mod
'up-to-date' is the definition.
(synonyms)
'second daughter' is the wordplay.
'second' becomes 'mo' (both are short periods of time).
'daughter' becomes 'd' (genealogical abbreviation).
'mo'+'d'='MOD'
'is' acts as a link.
(Other definitions for mod that I've seen before include "Rocker's rival?" , "ministry" , "Gaelic literary festival" , "1960s teenager" , "Meeting of the Scottish" .)