One place you can start to build mentoring into your agency’s culture, is at the top: Include mentoring in your senior leaders' performance agreements. That is, expect that every senior leader both has a mentor and is a mentor to a more junior employee as a part of their role in the company.
You can also host an easily accessible inventory of agency wide mentors and their particular expertise/discipline (wiki sites are good for this because employees can update it themselves). Encourage all employees to participate, not just the most senior ones. Since all employees have unique skills and capabilities, find a way to make it easy for colleagues to locate each other when they want to access a one-time answer or longer-term skill development.
Some organizations even host an annual or semi-annual “Mentor Week” to promote the benefits of informal mentoring for both the mentor (one of the best ways to retain or improve a skill is to teach someone else) and the mentoree (receive support and build a network).
On the coaching front instead of hiring expert coaches, offer interested employees training in basic coaching skills (listening, cultivating curiosity, and appreciative inquiry) and then create a peer coaching program with ongoing feedback mechanisms. This could consist of time-bound or topical peer coaching circles, hosting an informal inventory of peer coaches, or setting up a more structured and formal peer coaching program.
Above all, make coaching and mentoring an option in employee learning plans. Research shows that these activities are often much more useful towards developing skills and knowledge than formal training.