There are three approach known to de-extinction, the first involves breeding a living relative to have traits like the extinct animal (this was tried by breeding hairy Asian Elephants) here you won't have the DNA of the extinct animal but traits to fill in gaps in the ecosystem.

The second involves the genetic cloning which you mentioned, inserting the DNA in the egg of close relative, with that an animal with possible 100% identical DNA of the extinct animal might be gotten, but this has to be for a recently extinct animal to work very fine, this saw a goat giving birth to a pyrenean ibex(it later died from a lungs issue though), since it's been long the woolly mammoth went extinct, unsure of the possibility of that working for them.

Lastly is the option which is called genetic engineering (now being tried for them) , here the genome of the extinct animal is lined with that of it's living relative then relevant genes are swaped from the extinct to the living relative with genetic tools and the hybrid genome is grown in an artificial womb, this will not produce genetic identical copies of the extinct animal but a modern version of the engineered animal with traits of the extinct , don't know a percentage though.

I guess that answered your question @flyyingkiwi, nice stopping by :)