Are there any current efforts to clone recently (or soon to be) extinct animals?

Many scientists are trying to! As a matter of fact, they have a lot of mammoth and whooly rhino dna. They also have some dna from smilodon (saber-tooth tiger) recovered from tarmac ponds, dodo dna, and doedicurus dna. They have mostly mammoth and whooly rhino dna because it was preserved in the cool ice age ice.

And as to living but endangered species, they have plenty of gorilla dna.

Yes, as a matter of fact. There have been attempts to clone the 'supposedly' extinct Thylacine for a few years. There have even been attempts to try and clone the dodo.....

Try searching 'clone ______'