Let $\mathcal{B}$ be an extriangulated category which admits a cluster tilting subcategory $\mathcal{T}$. We firstly introduce notions of $\mathcal{T}$-cluster tilting subcategories and related subcategories. Then we prove there is a correspondence between $\mathcal{T}$-cluster tilting subcategories of $\mathcal{B}$ and support $\tau$-tilting pairs of $mod\underset{\_}{\mathrm{\Omega }(\mathcal{T}})$, which recovers several main results from the literature. Note that the generalization is nontrivial and we give a new proof technique.