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: $- mg\sin\theta\, \hat{\theta}$