Lightly sand with 180grit to remove any burs on the wood. I also knocked down the tips of the compass since I was planning to leather wrap.
Using a brush apply a water based glue to the wood ensuring to get into all the crevices.
White PVA glue will work. I used ecostick 1816b but there are many options.
lay out a thin piece of leather (I used 0.5mm Italian Buttero)
Starting from the middle press the leather into the details using your fingers.
The leather will stretch and conform as you gradually work it into the coaster.
Optional tools are a bone folder or smooth metal sculpting tool. but anything can work including a popsicle stick or bamboo skewer.
To finish the wrap stretch the leather around the edges and adhere it to the backside.
Trim any excess.
Adhere cork backing as desired. Enjoy!