As far as I know only one recording exists of Elvis performing this song. Elvis: "We've never done this live before". It's from Las Vegas December 11, 1976:
..
My heart can sing when I pause to remember
A heartache here is but a stepping stone
Along a trail that’s winding always upwards.
This troubled world is not my final home.
But until then my heart will go on singing,
Until then with joy I’ll carry on;
Until the day my eyes behold the city,
Until the day God calls me home.
The words and music of this song were written by Carl Stuart Hamblen (Oct. 20, 1908 - Mar. 8, 1989).
Stuart Hamblen was a well-known country-western singer and Hollywood actor in the 1930’s and 40’s. His popular radio program on the west coast of the United States "Cowboy Church Of The Air" made him radio’s first singing cowboy. The radio show ran from 1938 until 1952. He also played characters in ten western movies. At one point, he even ran for president of the United States–and did quite well on the west coast!
Hamblen was the son of a Methodist preacher, but seemed to turn his back on the values he’d been taught. However, during Billy Graham’s evangelistic meetings in Los Angeles, in 1949, Stuart Hamblen gave his heart to Christ. From then on, his life took a radical new direction.

Hamblen gave up his acting career and began an itinerant ministry for the Lord, bearing an effective testimony to the saving grace of God. He used his musical talent in a significant way in the Lord’s service, writing quite a number of gospel songs. It Is No Secret and Known Only To Him are the best known of these.
The original version of It Is No Secret as performed by Hamblen himself in 1950:
..
He wrote Until Then a couple of years later. In 1958 he recorded the song:
..
Ray Price recorded a beautiful version of the song for his album Faith in 1960.

..
Note: the song "Until Then" which he recorded for his last album in 2014, before he died, is a different song.
A more recent live version of the song (2012) as performed by Bill & Gloria Gaither ft. Jason Crabb:
..
SOURCES
http://davidneale.eu/elvis/originals/list9.html#S1533
https://www.youtube.com/watch?v=jGsa6rd_4rc
https://wordwisehymns.com/2013/08/09/until-then/
https://en.wikipedia.org/wiki/Stuart_Hamblen
.