Hard time for Greek goddess (4)
I believe the answer is:
hera
'greek goddess' is the definition.
(wife and sister of Zeus in Greek myth)
'hard time' is the wordplay.
'hard' becomes 'h' (abbreviation used in pencil classifications).
'time' becomes 'era' (an era is a period of time).
'h'+'era'='HERA'
'for' is the link.
(Other definitions for hera that I've seen before include "Wife of Jupiter" , "Divinity" , "Greek queen of Olympian gods" , "marriage goddess" , "Queen whose Roman counterpart was Juno" .)