Kain, 28, scored four tried in 18 appearances last year, while Clough joined the club from Gloucestershire All Golds in July.
Hawks director of rugby Darren Williams said: “Stuart is a very valuable member of our squad and is a rock in defence, he reads the game well, his positional play is exceptional as is his decision making.
“He is one of our longest serving players and a good guy to have around the place.”
“Lee just goes about his business with a no fuss attitude, does whatever is asked of him for the benefit of the team and his utility value was key last season as he slotted in at centre, wing and back row. He takes on every challenge that is presented to him and will be another valuable member of our 2014 squad.
“Chris knows he needs a good pre-season to get himself in good shape, if he does that he could have a good year as we all know he can certainly play but his fitness levels were not where they needed to be when he joined us mid season but he is aware of this.”