Foden and Palmer don't fit what you have described.
Foden was slowly introduced over 3 season period in the PL, playing 43 minutes, 327 minutes, 892 minutes, and bloodied in the cup before becoming a regular feature in the side.
Similar with Palmer, he's played 2 season in the PL playing 121 minutes followed by 358 minutes, similar in the cup competition for Man City, before becoming a regular at Chelsea.