At any moment, the tension force T minus m\vec{g} and Centripetal force force -mr\omega^2\hat{r} is the tangential component of force which drive the pendulum -mg \sin\theta \hat{\theta}
i.e. \vec{T}-m\vec{g}+mr\omega^2\hat{r}= -mg \sin\theta \,\hat{\theta}
So you can find \vec{T}= m\vec{g}-mg \sin\theta\, \hat{\theta}-mr\omega^2\hat{r}

or
Radial component: T=- (mr\omega^2+mg\cos\theta) \hat{r}
Tangential Component: - mg\sin\theta\, \hat{\theta}