Reading or writing, perhaps, in each period (3)
I believe the answer is:
era
'period' is the definition.
(I know that era is a type of period)
'reading or writing perhaps in each' is the wordplay.
'reading or writing perhaps' becomes 'R' (as in the traditional three R's of education).
'in' is an insertion indicator.
'each' becomes 'ea' (abbreviation).
'r' inserted within 'ea' is 'ERA'.
(Other definitions for era that I've seen before include "Important date" , "Important time" , "Long historical period" , "Eon" , "Are involved in time span" .)