Regular periods, including a day in Greek islands (8)
I believe the answer is:
cyclades
'greek islands' is the definition.
'cyclades' can be an answer for 'islands' (I've seen this before). I'm not sure about the 'greek' bit.
'regular periods including a day' is the wordplay.
'regular periods' becomes 'cycles' (cycle is a kind of period. I am not sure about the 'regular' bit.).
'including' indicates putting letters inside.
'day' becomes 'd' (abbreviation for day).
'a'+'d'='ad'
'cycles' placed around 'ad' is 'CYCLADES'.
'in' acts as a link.
Can you help me to learn more?
(Other definitions for cyclades that I've seen before include "Greek islands in the southern Aegean" , "Island group inc. Naxos" , "many islands" , "Aegean island group" .)