Yes, and that would definitely be the proper solution!
I had assumed a self-signed certificate been used, since it still has 8 years before expiring and it seems it’s already been in use for a while, but that’s a guess. If a certificate from a certificate authority had been used (and is now no longer functioning) then it should definitely be replaced with another certificate from a CA and not a self-issued certificate (though I’m surprised this issue would happen if the cert is from a CA).