An Agile Coach, is expected to be an expert of all Agile things like- frameworks, Agile practices, their implementations, Agile roles, soft skills, an epitome of leadership.
Based on the need of the hour and situation, he "lives in many hats" as listed inline:

When an Agile coach hones a teacher’s hat, he/she teaches as listed with a servant leader mindset:
-
Agile values and principles
-
The Agile roles
-
Frameworks or process as per the need. E.g., SAFe etc.
-
Techniques like estimations, story writing etc.
When an Agile coach hones a mentor’s hat, he/she:
-
Mentors teams who got used to Agile ways of working and focus on Agile practices.
-
Advice Scrum masters, Product Owners, facilitators on Agile Principles.
-
Mentoring teams/ individuals towards finding their solution rather than solving for themselves.
-
Knows when to switch between roles or wear hats and demonstrate the skills to help team stay on track.
-
Focuses for a long time duration and continuous development.
When an Agile coach hones a coaching hat, he/she:
-
Help teams to detect their own development stage.
-
Reinforce co-responsibility and be non-judgmental.
-
Coach different roles and make them self-aware, so that they keep “continuing” the “journey” as well surface the conflicts.
When an Agile coach hones a facilitator’s hat, he/she:
-
Defines clear outcome for the meeting/ session / event being facilitated.
-
Provides tools and techniques that aide in the outcome of the meeting.
-
Designs the activities for achieving the scope and purpose.
-
Maintains neutrality and suspends self-judgement.
Action task for readers: Self reflections and post your thoughts in the comments section
- What's your Coaching style?
- When encountered a situation in the team's Agile planning session, what style do you LIVE in?
- Which Atlassian product(s) do you use as a coach and why?
Source: My personal blog