Time up in which each copes successfully (5)
I believe the answer is:
epoch
'time' is the definition.
(I know that epoch is a type of geologic time)
'up in which each copes successfully' is the wordplay.
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'in which' indicates a hidden word.
'hcope' can be found hidden inside 'each copes successfully'.
'hcope' reversed gives 'EPOCH'.
(Other definitions for epoch that I've seen before include "Age, time span" , "Period of notable events" , "Significant period" , "years" , "significant time" .)