Yes, once you get off the plane (and into the terminal if you come into a bus gate) as you follow the connections signage, you'll have to go through another security screening as mentioned above. Nothing major, but I"ve been able to run right through it with nobody in front of us, and I've had it take nearly an hour to clear depending on how many are still waiting from the flight before yours.

I'm not sure where the WorldClub is located at NRT, but if it helps y'all in coordinating, the RCC is next to gate 31.

Enjoy your time in SIN, I love it there and looking forward to getting back for a night at the end of May. As others have mentioned, definitely head out for some local food at one of the hawker centres such as Lau Pa Sat or Newton.