What about UrlResolver?

As Valdis said. But I wanted to add that mapped URLs doesn't exist anymore, so your first code snippet doesn't make sense to handle in EPiServer 9 at all.

Yes Valdis, I figured it out that I can get ContentReference like:

var content = UrlResolver.Current.Route(new UrlBuilder(url));
if (content?.ContentLink != null)
{
var contRef = content.ContentLink;
}

But the problem is what would be the alternative for "PermanentLinkMapStore.ToPermanent" ?

As per Johan, it is true that "PermanentLinkMapStore.ToPermanent" has no sense in EPiServer 9, but what would be the safest way to replace existing code ?

Permanent links still exist. Mapped URL doesn't, which your first code snippet was referring to. So what are you trying to achieve, to mapped or to permanent?

You can try:

EPiServer.Web.Routing.UrlResolver.Current.GetPermanent();

or

EPiServer.Web.Routing.UrlResolver.Current.TryToPermanent();

to get a permanent link

Sorry Johan, what I referring was "PermanentLinkMapStore.TryToMapped" has no sense in EPiServer 9. 

OK. So I'll try with "PermanentLinkMapStore.TryToPermanent".  Actually my intention is to get Permanent Link here