Bits of old verse periodically appearing as part of today's theme (4)
'bits of old verse' is the definition.
'odes' can be an answer for 'verse' (I've seen this before). I'm unsure of the 'bits of old' bit.
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for odes that I've seen before include "Works by Pindar", "Verses", "Lays", "poetry", "Lines".)