1. It appears to be a bathtub drain not a shower.
2. You not only have a drum trap, but it is installed as an "S" trap.
3. As it sits, there is no way to make it legal or acceptable, because there is no vent, and any trap you install will automatically become an "S" trap, subject to all the problems that causes.
4. This is not a DIY job, and even a plumber could have problems installing it correctly.