Wa'alaykumsalam Wa Rahmatullah.
Yes It is permissible to hold the Quran and read from it while praying the Taraweeh or Tahajjud Prayer.
Aa’ishah (may Allaah be pleased with her) had a slave who used to lead her in prayer in Ramadaan, reading from the Mus-haf. Narrated by al-Bukhaari in a mu’allaq report (1/245).