Mounsey, the former Glasson Rangers amateur player and coach, has been on the Town board for three years.
“I’m delighted to have been elected Chairman,” Mounsey said.
“The club is busy regrouping for the new season in League 1 and with our very experienced Vice Chair Mark Fryer and a larger board, we are working hard to position the club to challenge for promotion in 2017.
“We’ve advertised for a new coach this week and have already had some strong interest.
“We will interview over the next couple of weeks and have our coaching set up sorted very shortly afterwards.
“Discussions with players are going well with our Director of Rugby Les Ashe and we will be announcing signings very shortly.
“Finances will be tight next season so the Board is looking at some ideas for regular fundraising.
“We are financially assisted by superb supporters groups like the Travellers Rest Supporters Club and the Ladies Committee and the club lottery and I’d like to pay tribute to them for their unstinting support.
“I’m personally looking forward to the challenges ahead. Our aim is for a locally based team and to build on the great work of our Community Trust to position the club at the heart of rugby league in West Cumbria.
“With the commitment of the Board, club staff and supporters we are optimistic about the future.”