Each piece of outsourced training work that is commissioned will require some degree of project management.
At one end of the scale you have major change programmes; with a defined L&D work stream that will be headed up by a work stream leader; who will commission activities in order to satisfy the overall programme.
Each of these activities may require a full time project manager to ensure that the deliverables meet the required time quality and cost criteria.
At the other end of the scale small pieces of work will be managed by the trainer who is responsible for designing and delivering the intervention.
Additionally, larger pieces of work can be sponsored from within the business or from within L&D. Should the work originate within L&D then clearly a sponsor will be required from within the business.
A key consideration here will be the amount of control you wish to retain initially; the amount of expertise within L& D and the amount of expertise within your outsource partner.