Mensa regularly announces tests (6)
I believe the answer is:
essays
'tests' is the definition.
(an essay is a type of examination or test)
'mensa regularly announces' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'announces' becomes 'says'.
The alternate letters of 'mensa' are 'es'.
'es'+'says'='ESSAYS'
(Other definitions for essays that I've seen before include "Tries to write compositions?" , "Tries for theses?" , "Literary efforts" , "Written works" , "Endeavours" .)