Hard time for goddess (4)
I believe the answer is:
hera
'goddess' is the definition.
(thesaurus)
'hard time' is the wordplay.
'hard' becomes 'h'.
'time' becomes 'era' (I've seen this before**).
'h'+'era'='HERA'
'for' is the link.
(Other definitions for hera that I've seen before include "Divine consort" , "Greek equivalent of Juno" , "marriage goddess" , "Jealous sister and wife of Zeus" , "female Greek deity" .)