  Charge density wave (CDW) states in solids bear an intimate connection to
underlying fermiology. Modification of the latter by a suitable perturbation
provides an attractive handle to unearth novel CDW states. Here, we combine
extensive magnetotransport experiments and first-principles electronic
structure calculations on a non-magnetic tritelluride LaTe$_{3}$ single crystal
to uncover phenomena rare in CDW systems: $(i)$ hump-like feature in the
temperature dependence of resistivity at low temperature under application of
magnetic field, which moves to higher temperature with increasing field
strength, $(ii)$ highly anisotropic large transverse magnetoresistance (MR)
upon rotation of magnetic field about current parallel to crystallographic
c-axis, (iii) anomalously large positive MR with spike-like peaks at
characteristic angles when the angle between current and field is varied in the
bc-plane, (iv) extreme sensitivity of the angular variation of MR on field and
temperature. Moreover, our Hall measurement reveals remarkably high carrier
mobility $\sim$ 33000 cm$^{2}$/Vs, which is comparable to that observed in some
topological semimetals. These novel observations find a comprehensive
explication in our density functional theory (DFT) and dynamical mean field
theory (DMFT) calculations that capture field-induced electronic structure
modification in LaTe$_{3}$. The band structure theory together with transport
calculations suggest the possibility of a second field-induced CDW transition
from the field-reconstructed Fermi surface, which qualitatively explains the
hump in temperature dependence of resistivity at low temperature. Thus, our
study exposes the novel manifestations of the interplay between CDW order and
field-induced electronic structure modifications in LaTe$_{3}$, and establishes
a new route to tune CDW states by perturbations like magnetic field.
