  In this Letter, we derive for the first time a characteristic three-peaked GW
signal within the framework of no-scale Supergravity, being the low-energy
limit of Superstring theory. We concentrate on the primordial gravitational
wave (GW) spectrum induced due to second-order gravitational interactions by
inflationary curvature perturbations as well as by isocurvature energy density
perturbations of primordial black holes (PBHs) both amplified due to the
presence of an early matter-dominated era (eMD) era before Big Bang
Nucleosythesis (BBN). In particular, we work with inflection-point inflationary
potentials naturally-realised within Wess-Zumino type no-scale Supergravity and
giving rise to the formation of microscopic PBHs triggering an eMD era and
evaporating before BBN. Remarkably, we obtain an abundant production of
gravitational waves at the frequency ranges of $\mathrm{nHz}$, $\mathrm{Hz}$
and $\mathrm{kHz}$ and in strong agreement with Pulsar Time Array (PTA) GW
data. Interestingly enough, a simultaneous detection of all three
$\mathrm{nHz}$, $\mathrm{Hz}$ and $\mathrm{kHz}$ GW peaks can constitute a
potential observational signature for no-scale Supergravity.
