The 41-year-old lacks the drive to compete in the sponsors’ race before Sunday’s British Grand Prix.
Clark called last year’s incident at Oakmont the “lowest point” of his career.
Van Poortvliet has edged Alex Mitchell.
The Lancashire seamer impressed in Wednesday’s Vitality series opener against India, which was washed out.
‘I will remember him as a fantastic jockey, but above all else the kindest man’.