The two well-known numerical radius inequalities for the tensor product $A \bigotimes B$ acting on $\mathbb{H} \bigotimes \mathbb{K}$, where $A$ and $B$ are bounded linear operators defined on complex Hilbert spaces $\mathbb{H}$ and $\mathbb{K}$, respectively are ${\frac{1}{2}}\mid\mid A\mid\mid\,\mid\mid B\mid\mid\leq w(A\bigotimes B)\leq \mid\mid A\mid\mid\,\mid\mid B\mid\mid$ and $w(A)w(B) \leq w(A \bigotimes B) \leq {\rm min}\{ w(A)\mid\mid B\mid\mid,\,w(B)\mid\mid A\mid\mid\}$. In this article, we develop new lower and upper bounds for the numerical radius $w(A \bigotimes B)$ of the tensor product$A \bigotimes B$ and study the equality conditions for those bounds.