Core component of racism I'd studied (5)
I believe the answer is:
Here is my best explanation:
'core' is the definition.
'component of racism i'd studied' is the subsidiary indication.
'component of' says the answer is hidden in the clue (I've seen this in other clues).
'midst' is hidden within 'racism id studied'.
(Other definitions for midst that I've seen before include "Where one is surrounded by other things", "Blue dye; rainbow hue", "Thick (of things)", "Centre", "Central part", "Among, amid" and "In the middle of (archaic or literary)".)