2, itself unfinished entering second day (10)
I believe the answer is:
backgammon
'2 itself unfinished entering' is the definition.
I can't tell whether this defines the answer.
'second day' is the wordplay.
'second' becomes 'back' (to second a motion is to back it).
'day' becomes 'gammon' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'back'+'gammon'='BACKGAMMON'
Can you help me to learn more?
(Other definitions for backgammon that I've seen before include "Board game played with dice" , "Dice and counter game" , "sedentary activity" , "Board game for two players" , "Players' race to clear tables" .)