Any thoughts about trust when bringing on a new employee with responsibility for crucial code of our software.

Security including protecting intellectual properties comes in layers. I have been employed by several people on different projects and these are some things I noticed my employers did to protect their work.
Limit access to codes
Have a strong employee contract
Have very clear employee policies
Log and maintain permission and access

If there's need for further clarification feel free to call.

Clear Goals and Objectives:

More often than not, it becomes difficult for employees to complete tasks without clear goals and objectives. Employees' work ethic also strengthens when they are fully aware of the work they are doing. Team leaders or managers should clearly explain the goals and objectives before they start new tasks. Irrespective of talent and work experience, employees need direction. Every organization follows a definite corporate ethical culture. Therefore managers need to align them with clear goals and objectives.

Hence, they can ensure the following points while they do it-

Goals should be measurable and maintain a fixed time frame.
It should be challenging and, at the same time, achievable.
It must be well accepted by the team members before implementation.

I think you can first sign a contract that keep your product confidential, and if he did not follow the contract, you can get a a sum of money for compensation(better be a lot, so he won't dare to steal the code). I suggest you get a lawyer for the paper works.