When elves die, their spirits go to the Halls of Mandos and are reincarnated/re-embodied after a certain amount of time. Glorfindel is the most famous case, but Finrod also "walks with Finarfin his father" according to the Silmarillion.
Not all elves are return to life. Feanor is still in the Halls of Mandos because of his crimes. Also, according to the Tolkien Gateway, Finwe refused to return to life so that Miriel may live again.
What about the other Noldor who died in Middle-earth, specifically the High Kings? Were they allowed to come back? If so, who would be the High King of the Noldor? Finarfin ruled the remnants of the Noldor after his brothers left, but Fingolfin was the High King after the death of Feanor, at least in Middle-earth. And there are other kings as well. If they were allowed to return to life, what would their status be?