Moncur, 19, made his first-team debut in West Ham's Capital One Cup win against Crewe earlier this season.
His father, John Moncur, made 205 appearances for the Hammers.
"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," Moncur told the club's official website.
"They've put their faith in me and I want to repay them by producing good performances out on the pitch.
"If I keep on doing what I'm doing then hopefully a first team chance will come."
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- John Moncur