Times keeps moving around a third anniversary (8)
I believe the answer is:
birthday
'anniversary' is the definition.
(I know that birthday is a type of anniversary)
'times keeps moving around a third' is the wordplay.
'times' becomes 'by' (both can mean 'multiplied by').
'keeps' indicates putting letters inside (inserted letters are kept inside).
'moving around' indicates an anagram.
'a'+'third'='athird'
'athird' is an anagram of 'irthda'.
'by' going around 'irthda' is 'BIRTHDAY'.
(Other definitions for birthday that I've seen before include "when one was delivered" , "Hardy bit (anag)" , "Invisible threads?" , "typically this suit amounts to nothing" , "It comes around once a year" .)