When a reed plate is loose due to brittle wax it is an indication that all the wax is brittle. But for starters you can try just the one reed plate and see how it goes.
First remove the pins, then pop out the loose reed plate. Scrape off any wax from the reed plate with a knife. You can use a knife, small screwdriver or any other small thing to scrape remaining was from the reed block. Try to get it all off without damaging the wood, but also without causing the adjacent reed plates to come loose. I use what I call a "pinger" which is a steel flat tool used for holding the reed while tuning. Afterwords the pinger needs to be thoroughly cleaned with naphta before using it again as a pinger. All tools you use need to be cleaned with naphta to remove any trace of wax.
How to wax in the new reed (good method for beginners): for starters, have the leather or plastic valve on the side of the reed plate that goes on the inside of the reed block and leave the valve off on the outside.
Cut a small strip of wax from a block of accordion wax, and roll it between your fingers so it is long round and thin (a bit thicker than a toothpick). Warm a soldering iron to maybe 70 or 80 degrees centigrade (use a dimmer to lower the power of the iron). You can melt a drop of wax on the base of the reed block and slide and press the reed plate onto it so it stays temporarily in place. Then melt some wax to bond the top side of the reed plate with the reed block (so the reed plate is now "connected" to the reed block on two ends). Make sure all of this is done without getting any wax between the reed plate and the wood: the plate needs to lay flush on the wood.
Then for the tricky bit: the wax in between the reed plates. I'm assuming you have at list half a millimeter of room here (a different technique is needed for reed plates that almost touch each other in extremely compact instruments). Cover the edges of the reed plate and the adjacent reed plate with painters tape, leaving only the empty space between the reed plates exposed. Now melt some wax to flow into the opening between the reed plates. Fill up the space but don't fill more than that. If there is too much wax (a "mountain"), remove it by sliding a small screwdriver through the (top of the) space between the reed plates. Remove the painters tape. Repeat the process for the space between the reed plate and the other adjacent reed plate. Then melt some wax around the base so the gap between the "base" edge of the reed plate and the reed block is filled up. Maybe melt the existing wax around the top edge for a nice, professional looking, finish.
Then clean the reed plate thoroughly with a paper towel soaked in naphta.
Finally, glue the valve that goes on the outside. You can choose to put the pins back, or not.
It takes longer to write all this down than to actually do it...
What I found very instrumental in successful waxing (which I do with the Italian spoon method, just "finishing off" using a soldering iron) is that you first leave the valve off and that you cover the reed plate edges with painters tape. When wax gets on the reed plate, or worse, on the reed, it is a mess to clean up with naphta. Much better to avoid it in the first place.
One final important word of advice: once you have the reed plate waxed in and the reeds are working properly, do not consider tuning for at least 2, better 3 weeks. The wax needs to harden and the tuning will change in this period.