The 31-year-old has played in all four divisions for the club, plus the triumphant Capital One Cup success of 2013, and signed a new one-year contract extension on Wednesday
The 31-year-old midfielder has played in all four divisions with the Swans in the English football pyramid and extended his contract by 12 months on Wednesday, committing himself to the club until 2017.
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"The way he plays, the effort he puts in every day - he is an example to others in the squad. It's massive for us to get Leon's contract sorted out because he is such an important player."
Monk is hopeful that captain Ashley Williams will now follow Britton's lead in extending his stay at the club.
The centre-back has an extra year to run on his current deal, and has been linked with the likes of Arsenal and Napoli.
"Hopefully Ash will follow suit," he added. "He is another one who is vitally important to us going forward. These are players who represent all the values that are good about Swansea City.
"They have played a huge part in the success we've had and we want them here for the future as well.
"Younger players and players we bring into the club need to look at players like Ash and Leon and see how they work.
"They can help educate the players we bring in. They can show them what it means to play for Swansea City."