As the product owner, what is the best approach to administering the scrum framework in vendor-led app development? And eliminate the difficulty of ensuring they build and deploy in line with a sprint goal.
This is less a question about agile and more of a vendor relationship question. If you hire a vendor to develop software, they have some process for doing that. If they develop software using Scrum or XP, then you should have discussed how they do that in the vendor selection process.
Now, one of the problems I see with some frequency is that a client says "we want this to be agile" and the vendor says "yeah, so, no problem" because they want to contract. Then someone on the client side is left trying to figure out how to get the vendor to "be agile".
If this is the situation you are finding yourself in, you may need to go back to the original vendor agreement and have a discussion about it - do they use scrum for building their software or not? Are both of your understandings of Scrum the same? The likelihood that you will be able to effectively get them to reorganize their business to a more agile way or working is very low.
Scrum is very attractive as a way of managing a vendor relationship. A prioritised backlog provides good transparency and iterative delivery helps minimise the risk. Vendor selection is important though so make sure they are experienced with Scrum and willing to use it.
Keep sprints short (2-3 weeks is usually good). Make the most of the collaborative approach by getting stakeholders involved during sprints and at reviews. The vendor won't know your business as well as an insider would so the stakeholder feedback is essential. Also do plenty of backlog refinement and story mapping to keep a picture of the longer term roadmap.