There is no such service. Tenebrae belongs to the Paschal Triduum - i.e. on Maundy Thursday, Good Friday, and Holy Saturday. The Tenebrae service for Maundy Thursday is often held on the Wednesday evening rather than in the early morning of the Thursday to better accommodate the faithful. It is the longest of the three Tenebrae services - largely due to the longer psalms appointed in the matins.
eBreviary is a fee-based subscription service for daily booklets for the Liturgy of the Hours. However, they also have a bunch of free stuff on their website, including Tenebrae booklets for Good Friday and Holy Saturday.
Using these liturgies as a model, one could combine their Holy Thursday booklets for the Office of Readings and Morning Prayer into a single booklet for Holy Thursday's Tenebrae.
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