If no, then is there any way to connect a clearnet website, hosted on shared web hosting, with a .onion domain name?
Probably not. You need command line access to the operating system to be able to set up tor to work with your site. That's if they even have Tor installed. Neither is very likely.
No, but you can have the website and the Onion's Tor daemon on different servers and make the Onion daemon connect to your website. You can do that by putting the destination IP address and port in the HiddenServicePort config option on the torrc file, as described in the Onion service guide:
HiddenServicePort 80 198.51.100.1:8080
I am not sure whether domain names work instead of IP addresses but, in the case they don't, you can always set up a reverse proxy like Nginx on the same server as the Tor daemon to forward the requests without having to pay extra to your web hosting provider for a dedicated IP address.