Councillor Mollett had represented the Horsehay and Lightmoor ward since 2008.
He held a number of posts in the council's administration until 2011, including cabinet assistant for children and young people and vice chair of appeals. He also served on a number of committees since 2011.
Councillor Mollett also served as a governor at Lightmoor Village Primary School.
Richard Partington, Telford & Wrekin Council's managing director, said: "I am sure that I speak for everyone at the council when I say how sad we are to learn of Clive's passing. Our thoughts are with his family at this sad time."
Council leader Councillor Shaun Davies said: "I was very saddened to learn of Councillor Mollett's death.
"He has served the council and the community well and he will be missed by all councillors from across the political spectrum."