Looking at the Latin Liturgia Horarum (2000) and the General Instruction on the Liturgy of the Hours, I haven't found any directive to suppress the Gloria Patri during the Triduum. Unless someone finds such a rubric, I will suppose the GP is required as usual.
In the traditional office, the Gloria Patri is suppressed from Holy Thursday ad Matutinum through the Vespers of Holy Saturday.
@chonak is right - in post-conciliar Liturgy of the Hours there are no Tenebrae in proper sense and there is no suppression of Gloria Patri, either. (Neither in Triduum, nor in Officium defunctorum.)
In the post-conciliar monastic Office, the old rubrics have been retained. No opening verse (launch directly into the psalms), no hymn, and no concluding verses (Office ends with the collect). No mention of the GP though so I assume it is still said. See Antiphonale Monasticum published by Solesmes in 2005.
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