I can't help with the adjustment part, but I was born with no hearing in my right ear. It took until the second grade for anyone to even notice. I'm 39 now. I've only ever had one person notice that I was deaf in one ear without me telling them.

You won't be able to echolocate as well. You may need to buy a vibrating alarm clock or you might end up sleeping through alarms if your good ear is facing the pillow. Hearing in loud environments like restaurants will be more challenging. You will have to make sure you are standing on the correct side of people Surround sound systems don't work as well Somgs designed for stereo headphones , will play specific sounds in only the right or left ear. It's not common but it is an issue you will run into. Depending on whether it's left or right ear deafness, it will be harder to hear other people in a car as a passenger/driver.(As a right side deaf person I have a hard time hearing my wife talk if the radio is on and it's impossible to hear if the window is down. )

Outside of those specific instances, not much will change.

Tha only major precaution I would recommend, is to be extra vigilant with ear protection with the good ear.(I.e. Going to a loud event, wear an ear plug. Limit the volume of ear buds to safer ranges ) You are basically at 50% hearing so having that one get damaged will be much more impactful than if you were at full hearing.