Period of time in which duke meets lady occasionally (3)
I believe the answer is:
day
'period of time' is the definition.
(day is a kind of period of time)
'duke meets lady occasionally' is the wordplay.
'duke' becomes 'd' (abbreviation).
'meets' means one lot of letters go next to another.
'occasionally' indicates alternate letters.
The alternating letters of 'lady' are 'ay'.
'd'+'ay'='DAY'
'in which' is the link.
(Other definitions for day that I've seen before include "24 hour period" , "Unit of time" , "24 hours" , "24-hour period" , "Twenty-four hours" .)