Tiny part of the day (6)
I believe the answer is:
minute
This clue is a double definition.
'tiny' is the first definition.
(thesaurus)
'part of the day' is the second definition.
('minute' is part of 'day')
(Other definitions for minute that I've seen before include "Tiny; written note" , "Little - bit of time" , "Very short or tiny" , "barely noticeable?" , "Tiny - proportion of time" .)