A fan of any anthem from time to time, say (8)
I believe the answer is:
intonate
'say' is the definition.
(I've seen this before)
'a fan of any anthem from time to time' is the wordplay.
'a fan of' becomes 'into' (I've seen this before).
'from time to time' indicates alternate letters (letters removed on a regular basis).
'any'+'anthem'='anyanthem'
The alternate letters of 'anyanthem' are 'nate'.
'into'+'nate'='INTONATE'
(Other definitions for intonate that I've seen before include "say" , "chant solemnly" .)