The midfielder has penned a two-year deal, with an option for a third, with the club.
Moncur, the son of former West Ham and Tottenham midfielder John Moncur, said: "I am over the moon to have signed my new contract. It is great to play at this football club, so to sign for another two years is really great for me and my development.
"Hopefully it will continue to go as well as it has so far. They have put faith in me and I want to repay them by putting some good performances out on the pitch.
"If I keep on doing what I am doing then hopefully a first team chance will come. Obviously my old man played here for quite a while, so it would be nice to follow in his footsteps and make that progression to the first team."