Periodically fancy that series of old deeds (4)
I believe the answer is:
acta
'series of old deeds' is the definition.
(historic term for a collection of records)
'periodically fancy that' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
'fancy'+'that'='fancythat'
The alternate letters of 'fancythat' are 'ACTA'.
(Other definitions for acta that I've seen before include "records" , "minutes of official proceedings" .)