Long periods of recounts, periodically (4)
I believe the answer is:
eons
'long periods' is the definition.
(I've seen this in another clue)
'recounts periodically' is the wordplay.
'periodically' indicates alternate letters (letters must be selected 'every so often').
The alternating letters of 'recounts' are 'EONS'.
'of' acts as a link.
(Other definitions for eons that I've seen before include "Years and years" , "Endless periods" , "Long periods of time - noes have it" , "Times" , "Divisions of archaeological time" .)