During travels notice region centred on Delos (8)

I believe the answer is:

cyclades

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'region centred on delos' is the definition.
I can't judge whether this defines the answer.

'during travels notice' is the wordplay.
'during' is an insertion indicator.
'travels' becomes 'cycles' (I can't justify this - if you can you should believe this answer much more).
'notice' becomes 'ad'.
'cycles' enclosing 'ad' is 'CYCLADES'.

Can you help me to learn more?

(Other definitions for cyclades that I've seen before include "many islands" , "Greek islands in the southern Aegean" , "Island group inc. Naxos" , "Aegean island group" .)

I've seen this clue in The Times.

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