My phone says that my watch needs a software update but then it says it’s done and nothing happens. It won’t pair

To remove the watch from your wife's account;

What to do before you sell, give away or trade in your Apple Watch

Then;

Set up and pair Apple Watch

What model of phone is it and what version of ios is it running?

What model of watch is it and what version of WatchOS is it running?.

What troubleshooting steps have you tried?.

What errror messages are you receiving?.

Has this watch ever been paired to another phone?(Very important).