  In this paper, we will show vanishing theorem of $p$ harmonic $1$ form on
submanifold $M$ in $ \bar{M} $ whose BiRic curvature satisfying $
\overline{\mathrm{BiRic}}^a \geq \Phi_a(H,S) $. As an corollary, we can get the
corresponding theorem for $ p $ harmonic function and $ p $ harmonic map. We
also investigate the finiteness problem of $p$ harmonic $1$ form on submanifold
$M$ in $ \bar{M} $ whose BiRic curvature satisfying $
\overline{\mathrm{BiRic}}^a \geq -k^2 $.
