It's not hard to understand why the New Testament might resonate more strongly for the cultivation of relics than the Old Testament over the centuries of the Church's history. To name a few:
- The Holy Grail
- The Spear of Destiny
- The Stone of Unction (once resided in Ephesus)
- The True Cross
- The Holy Girdle (and other Marian relics)
- Bones of the Saints
Many of these New Testament relics hold clear theological and soteriological significance.
With regard to why early Christian institutions (Byzantine Church, Roman Church, as well as quasi-autonomous monasteries) have not devoted resources to the acquisition of Old Testament relics, I can think of two major factors:
- Preservation bias (the Old Testament happened a long time ago)
- Less straight-forward interpretation
This scholarly work lays out some of the thinking behind the acquisition of relics in Byzantium, how they were collected and what divine influence they were expected to provide. The focus is clearly on Passion relics and virtually nothing on relics from the Pre-monarchistic period or Post-exilic period that bookends the Old Testament.
The closest thing I was able to find was featured in a different monograph from Brill Publishing, titled The Paintings of the Pre-Islamic Kaaba. Here the author highlights that the Kaaba once housed ram horns believed to originally have belonged to the ram that Abraham sacrificed in place of Isaac. While the time period is concurrent with Christian relic acquisitions, it's an Islamic view on the sanctity of an Old Testament relic. Moreover, I have not encountered any Christian institution that had an expressed interest in acquiring the ram horns of Abraham's sacrifice.
Taking the general direction of my above research, what evidence do we have for the existence of Old Testament relics that were sought after by the early Church(es)? Not including the Ark of the Covenant, which is rather ubiquitous.