The eight safety representatives at the company were nominated for the award after they negotiated a joint strategy and approach to health, safety and environmental issues at the Fife-based mill.
Malcolm Sinclair, marketing director at TR, said: "There's been a real improvement in team working, and we are delighted and proud of their efforts."
The safely representative's role includes checking that the employer also carries out its responsibilities.
Debbie Hutchings, Unite regional official, said the STUC award is recognition that safety reps have a major role.
She said: "We have seen that where safety reps are involved in an organisation's safety management, this benefits all."
Government cuts to the Health and Safety Executive over the next few years will "cause untold problems for representatives on the frontline", according to Hutchings.
"We hope these awards will encourage reps to strive for better conditions and involvement in the future," she added.