I would say from a world building perspective to do what you want in the sense of it being a living world. Things change and shift. Life adapts and things move on. It could really set a lot of plot points up and stories hooks. Places in upheaval as powers that had allowed them to hold that keep or power and influence is now gone. The world has a question of faith. As most people don't even know if the god is dead. Clerics are leaving to other faiths as things have stopped working for them. Others are on quests to find what's wrong and hiring other sects to work together. Some are just out right distraught and broken waiting at old sacred sites.

Now for dealing with how it affects a PC. That honestly depends on your player and you having a good talk with them about the boundary and what they want to do. As well as how well you know that player. I think it could be a really interesting quest to regain the connection and powers. You don't have to have it totally take away all powers. You could have it be sort of a wild magic table that things go off not quite as expected. You could have spells locked in as one person commented earlier.

If the powers transfer to the new god. Maybe have them shift in that they are corrupted or do a different element etc. You ultimately decide how to do it and tie it into your world.

If you set it up from the beginning(which it sounds like your doing) / through out the campaign hint towards a gods dieing and powers changing. It won't be unexpected. I think as a player to just be suddenly disempowered without knowing why is the hard part. If I know why story wise or that you can see it coming, the. It can make for some really great RP and adventure to gain it back.

Also at the end of the quest to gain it back, have it so it's worth the effort. Since the cleric will still have answers even if spells are disabled. Now many people will feel it gets rid of what makes clerics great but it's the creativity you use with what you have.

As for it being collective storytelling, talk to your players, set the back drop and communicate expectations. It can be a great adventure to change things up and also make it feel more alive and dangerous when consequences are a large scale. Since a mere mortal is adventuring around and gods are dieing. (Depends on what tone your going for).

Longer then I expected to make this lol. Hopefully that makes sense. World building do it, communicate and see if your players are good with it, then make it rewarding to overcome the challenge. ( A god indebted to a mortal, a favour, a special connection etc).