Burden of testing periodically brought up (4)
I believe the answer is:
gist
'burden' is the definition.
('gist' can be a synonym of 'burden')
'testing periodically brought up' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
'brought up' shows that the letters should be reversed in order (down clues only).
The alternate letters of 'testing' are 'tsig'.
'tsig' reversed gives 'GIST'.
'of' acts as a link.
(Other definitions for gist that I've seen before include "General meaning or main point" , "Main point of the matter" , "Key point" , "Core meaning" , "Substance of an argument" .)