Midfielder Kay missed the recent 3-0 defeat at Norwich - the Boxing Day clash at Carlisle was postponed - through suspension, but is expected to return at the expense of Jim Goodwin.
Versatile Clarke is back in the reckoning following minor knee surgery, while Drinkwater, on loan from Manchester United, has shaken off a thigh strain that forced him to miss 12 matches.
Terriers boss Clark has a fully-fit squad to choose from following striker Robbie Simpson's recovery from a similar thigh problem, with no new injury or suspension worries.
Town hope to bounce back from defeat at Carrow Road, their second in nine league games, in order to maintain their promotion challenge.
