  We investigate emergent quantum dynamics of the tilted Ising chain in the
regime of a weak transverse field. Within the leading order perturbation
theory, the Hilbert space is fragmented into exponentially many decoupled
sectors. We find that the sector made of isolated magnons is integrable with
dynamics being governed by a constrained version of the XXZ spin Hamiltonian.
As a consequence, when initiated in this sector, the Ising chain exhibits
ballistic transport on unexpectedly long times scales. We quantitatively
describe its rich phenomenology employing exact integrable techniques such as
Generalized Hydrodynamics. Finally, we initiate studies of
integrability-breaking magnon clusters whose leading-order transport is
activated by scattering with surrounding isolated magnons.
