We're usually expensive, so this is a fair question :) .
I've addressed this elsewhere, where I've humbly submitted the following:
I measure how we are doing as Agile Coaches, in part, by focusing on the conducting of product experiments by Product Owners, and process experiments by Scrum Masters.
Later, I added specificity to the thought as it applied to Scrum Masters, proposing:
“new process experiments over time” as the meta-metric uniquely aligned with the Scrum Master role, which can be a leading indicator for the other metrics
If the above does not jive with you, that's great. Seriously. This means you have an idea in your head of what an Agile Coach should be doing, and how their presence should be adding value to your organization. Let's hold on to your idea.
Because Agile Coaching is still a relatively new profession, there is some variability as to what this person does.