Clark and Thorley will both be unavailable for the Champions Cup games away at Edinburgh on Friday and at home to Toulon on 17 January, as well as the Prem game at home to Bath on 23 January (Thorley subject to completing CIP).
Clark had only returned from a period out injured for Gloucester in mid-December, starting their past three games.
Thorley scored a try in the loss to Newcastle before his red card, one of three in 11 games so far this campaign.
Gloucester have just one win all season in the Prem and are second bottom, above Newcastle by virtue of four bonus points.
