Modern-day study on vitamin ...er... supplement (8)
I believe the answer is:
addendum
'supplement' is the definition.
(I know that supplement can be written as addendum)
'modern-day study on vitamin er' is the wordplay.
'modern day' becomes 'AD' (AD, Anno Domini, as opposed to BC, Before Christ).
'study' becomes 'den' (term for a study or office).
'on' is a charade indicator (letters next to each other).
'vitamin' becomes 'D' (D is an example).
'er' becomes 'um' (both are expressions of uncertainty).
'ad'+'den'+'d'+'um'='ADDENDUM'
(Other definitions for addendum that I've seen before include "Something attached to the end, say of book" , "Supplement, appendix" , "Missing passage to be appended" , "it wasn't there originally" , "Extra piece of text" .)