A December 1973 publication by the Australian Episcopal Conference "Music in the Liturgy: a directory and list of approved music for the sung liturgy" has on page 7:
"5. The GRADUALE SIMPLEX (3rd September 1967) – The Simple Gradual using simpler Latin Gregorian-style chant melodies is referred to in the General Instruction in the same numbers cited above.
The ICEL translation became available in 1968. This translation has been officially approved for use in Australia."
This is part of a list of "the various sources of liturgical texts mentioned in the General Instruction on the Roman Missal
". Also listed is "3. The GRADUALE ROMANUM December 1907, in Latin with Gregorian chant melodies. The Roman Gradual is cited in the General Instruction in nos. 36, 37, (50), 56i. ...".
I am fairly sure that the translation of Graduale Simplex being referred to is "The Simple Gradual for Sundays and Holy Days Full Music Edition for Cantor, Choir and Organist". Edited by John Ainslie. Published by Geoffrey Chapman. It has near the front:
"First published, 1969
Concordat cum originale; John Humphreys, Secretary of National Liturgical Commission of England and Wales, 20 December 1968."
This "Concordat cum originale" is part of translations of liturgical books, saying that is a correct translation. But this translation is different to other official liturgical books I am familiar with. There is no decree at the front. The is no translation of the praenotanda, or general instruction. (This can be found in Documents on the Liturgy 1963-1979, Liturgical Press, Minnesota, 1982, ISBN 0-8146-1281-4, page 1340.) But it has on page vi "This English edition of the Graduale Simplex
covers all Sundays and Holy Days of Obligation".
Here is an outline of the contents for one Mass, Advent Season I, on pages 1-4:
11. Entrance song with music for Antiphon.
12. Alternative antiphon
From Psalm 24, with pointing for singing using Gelineau psalmody, Murray psalmody and Bevenot psalmody. (Psalm tones for these are provided in a card with the book.)
13. Responsorial Psalm, from Psalm 70, with pointing for Murray psalmody but not Gelineau.
14. Alleluia Psalm, from Psalm 84, with pointing for Murray psalmody but not Gelineau.
17. Offertory Song, from Psalm 24, with pointing for Gelineau, Murray and Bevenot psalmody.
18. Communion Song, from Psalm 84, with pointing for Gelineau, Murray and Bevenot psalmody. It has "Alternative communion song: No. 330."
there is available for "Simple English Propers: For the ordinary Form of mass Sundays and Feasts". Published in 2011, this is provided for free, under Creative Commons Licence. In its introduction it has about the importance of sung propers:
"This is why the General Instruction on the Roman Missal (GIRM) speaks of adding decorum to the processions (entrance, offertory, and communion) by singing the “chants proper to them” (44). “After the people have gathered, the entrance chant begins” (47).“The procession bringing the gifts is accompanied by the offertory chant, which continues at least until the gifts have been placed on the altar” (74).“While the priest is receiving the Sacrament, the Communion chant is begun” (87)."
It does not include the Responsorial Psalm or Alleluia Psalm found in The Simple Gradual edited by John Ainsle.
The GIRM has:
"61. ... Instead of the Psalm assigned in the Lectionary, there may be sung either the Responsorial Gradual from the Graduale Romanum
, or the Responsorial Psalm or the Alleluia
Psalm from the Graduale Simplex
, as described in these books." (Roman Missal, English translation according to the third typical edition, approved for use in the dioceses of Australia, England and Wales, and Scotland, published by Catholic Truth Society, in 2010, ISBN 9781860827303, page 44.)
At least in Australia, I think this means there can be singing of these psalms in Latin from Graduale Romanum, or in English from the The Simple Gradual edited by John Ainsle.