The central defender, who joined the club on loan from Manchester City in August, has yet to play for the first team.
He will turn out for the B side this evening, however, as they travel to face East Fife in the Challenge Cup.
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Callum Osmand, also signed in the summer, has been handed the nod, too, with the striker netting in each of his appearances for the Bhoys' second team so far.
Kick-off at Bayview is at 7.45pm.
Team news from Bayview 🔢
Here is how the young Hoops line-up for this evening's KDM Evolution Trophy match against East Fife 📋⤵️#EASCEL | #CelticFC🍀 pic.twitter.com/aIOHrVtVdv
— Celtic FC B (@CelticFCB) October 10, 2025
Speaking on Simpson-Pusey's situation at Celtic last month, manager Brendan Rodgers said: "I think it was a medium to longer-term signing we were looking at with young Jahmai.
"We had our centre-halves in place, but he was a young player who we saw as a talent. He has come in, but the team have defended well in the main. He is here for the 12 months, at least, to show what he can do.
"It is not easy to come into a club like Celtic, because you still have to earn your position in the team. You're coming into a new environment from his club, so it just takes time - it is that adaptation.
" Liam Scales and Cameron Carter-Vickers have been doing really well. Dane Murray has been great over the course of pre-season. We've still got Auston Trusty , who is just coming back from injury.
"The competition is there, and you have to earn your place. I'm really pleased with his development and how he has been moving in the right direction with adapting to the intensity of how we work and play, as well as moving away from Manchester.
"I'm pretty sure that over the course of the season, when that opportunity comes, he'll be ready."