Is this devotion older than the Litany of the Holy Spirit?
Did you mean Litany or Novena? If Novena, yes, it's the
oldest novena,
The novena in honor of the Holy Ghost is the oldest of all novenas since it was first made at the directions of Our Lord Himself when He sent His Apostles back to Jerusalem to await the coming of the Holy Ghost on the first Pentecost.
The above novena petitions for gifts in this life. It does gain indulgences, yet it may not be the
oldest indulgenced devotion if age is counted from when those indulgences first received papal approval. The link above quotes Pope Leo XIII though it's not clear from the web sources I could find whether his papacy is when it happened.
Also there's a Franciscan Capuchin
Chaplet for private use that dates to 1892/1902.