  We construct a new model for relativistic particle on the noncommutative
surface in $(2+1)$ dimensions, using the symplectic formalism of constrained
systems and embedding the model on an extended phase space. We suggest a short
cut to construct the gauged Lagrangian, using the Poisson algebra of
constraints, without calculating the whole procedure of symplectic formalism.
We also propose an approach for the systems, in which the symplectic formalism
is not applicable, due to truncation of secondary constraints appearing at the
first level. After gauging the model, we obtained generators of gauge
transformations of the model. Finally, by extracting the corresponding Poisson
structure of all constraints, we show the effect of gauging on the canonical
structure of the phase spaces of both primary and gauged models.
