  We present a study of $\tau^+ \tau^-$ lepton pair production in Pb + Pb
collisions at $\sqrt{s_{NN}}$ = 5.5 TeV. The larger mass of tau lepton compared
to electron and muon leads to considerably small hadronic contribution to the
$\tau^+ \tau^-$ pair invariant mass (M) distribution relative to the production
from thermal partonic sources. The quark-antiquark annihilation processes via
intermediary virtual photon, Z and Higgs bosons have been considered for the
tau lepton production. The contribution from Drell-Yan process is found to
dominate over thermal yield for $\tau^+ \tau^-$ pair mass from 4 to 20 GeV at
the LHC energy. We also present the ratio of $\tau$ lepton pair yields for
nucleus-nucleus collisions relative to yields from p + p collisions scaled by
number of binary collisions at LHC energies as a function $\tau$ lepton pair
inavariant mass. The ratio is found to be significantly above unity for the
mass range 4 to 6 GeV. This indicates the possibility of detecting $\tau^+
\tau^-$ pair from quark gluon plasma (QGP) in the mass window 4 to 6 GeV.
