Little kindergarten’s opening in seven days (4)
I believe the answer is:
week
'seven days' is the definition.
(I've seen this before)
'little kindergarten's opening' is the wordplay.
'little' becomes 'wee' ('wee' can be similar in meaning to 'little').
'opening' says to take the initial letters.
The initial letter of 'kindergartens' is 'k'.
'wee'+'k'='WEEK'
'in' is the link.
(Other definitions for week that I've seen before include "Period of time; sounds like feeble" , "Part of the year" , "Calendar period" , "A long time in politics?" , "Seven days" .)