  We derive necessary and sufficient conditions for the existence of the exact
solution to the Sylvester-type quaternion tensor system $
\mathcal{A}_i\ast_{N}\mathcal{X}_i+
\mathcal{Y}_i\ast_{M}\mathcal{B}_i+\mathcal{C}_i\ast_{N}
\mathcal{Z}_i\ast_{M}\mathcal{D}_i+\mathcal{F}_i\ast_{N}
\mathcal{Z}_{i+1}\ast_{M}\mathcal{G}_i=\mathcal{E}_i, i=\overline{1,3} $ using
Moore-Penrose inverse, and present an expression of the general solution to the
system when it is solvable. As an application of this system, we provide the
solvability conditions and general solutions for the Sylvester-type quaternion
tensor system $ \mathcal{A}_i\ast_{N}\mathcal{Z}_i\ast_{M}\mathcal{B}_i+
\mathcal{C}_i\ast_{N}\mathcal{Z}_{i+1}\ast_{M}\mathcal{D}_i= \mathcal{E}_i,
i=\overline{1,4}. $ This paper can also serve as extensions to some known
results.
