Recess to include unexpected third anniversary (8)
I believe the answer is:
birthday
'anniversary' is the definition.
(I know that anniversary can be written as birthday)
'recess to include unexpected third' is the wordplay.
'recess' becomes 'bay' (bay is a kind of recess).
'to include' is an insertion indicator.
'unexpected' indicates anagramming the letters.
'third' anagrammed gives 'irthd'.
'bay' enclosing 'irthd' is 'BIRTHDAY'.
(Other definitions for birthday that I've seen before include "It comes around once a year" , "typically this suit amounts to nothing" , "Nothing to wear?" , "when one was delivered" , "Invisible threads?" .)