By definition, a level set of contact type admits a contact form obtained by contracting the Hamiltonian vector field into the symplectic form. In this case, the Hamiltonian flow is a Reeb vector field on that level set.
A level set of contact type can be used to create a contact form through the application of the Hamiltonian vector field to the symplectic form. The resulting Hamiltonian flow is a Reeb vector field on that level set.