  It is an intriguing question how local time can be introduced in the emergent
picture of spacetime. In this paper, this problem is discussed in the context
of tensor models. To consistently incorporate local time into tensor models, a
rank- three tensor model with first class constraints in Hamilton formalism is
presented. In the limit of usual continuous spaces, the algebra of constraints
reproduces that of general relativity in Hamilton formalism. While the momentum
constraints can be realized rather easily by the symmetry of the tensor models,
the form of the Hamiltonian constraints is strongly limited by the condition of
the closure of the whole constraint algebra. Thus the Hamiltonian constraints
have been determined on the assumption that they are local and at most cubic in
canonical variables. The form of the Hamiltonian constraints has similarity
with the Hamiltonian in the c < 1 string field theory, but it seems impossible
to realize such a constraint algebras in the framework of vector or matrix
models. Instead these models are rather useful as matter theories coupled with
the tensor model. In this sense, a three-index tensor is the minimum-rank
dynamical variable necessary to describe gravity in terms of tensor models.
