Hi there! Thanks for providing this information. I've updated the A record on our end to point to the new IP address. However I am still seeing a 403 error occur on the site. When looking at the site directly from the host IP address, though, it appears the site has some malware blocking access to the site. I would recommend using a security plugin such as Wordfence to address this issue first as this is most likely the cause of the error you are seeing.
I did also notice that there are still some hostinger addresses in your DNS records, which may cause additional conflict. Could you please look through your DNS records and remove any hostinger-related records, and possibly update them with the records from your new host if there are any new ones? The malware should definitely be addressed first but the old hostinger addresses in your DNS records would need to be addressed as well.