Very early, having time (4)
I believe the answer is:
year
'time' is the definition.
(year is a unit of time)
'very early having' is the wordplay.
'having' indicates a hidden word.
'YEAR' can be found hidden inside 'very early'.
(Other definitions for year that I've seen before include "See 33 Across" , "Group of students" , "Full calendar?" , "Orbital period" , "One intake of undergrads" .)