When I took my present job, my boss set a goal for me that involved improvements in another department. When I pointed out that I had no control over that goal, he said, "I expect you to use influence where you don't have authority."
In other words, lead my peers. That's the truest form of leadership, getting people who don't have to listen to you to do what is needed.
Peers will follow you if a couple of conditions exist.
First, they can't see you as a threat, to their position, prestige, or chances of promotion. Most of us have the idea that we have to out-compete our peers for the good stuff. If they think you're trying to gain an advantage in the rat race, they'll never follow.
Second, what you're proposing has to make sense for them. It should make life easier for them or their department in some way; there needs to be an advantage. Otherwise, why spend their resources on your problem? You can't expect peers to follow just because you or your boss wants them to.
So here are the to-dos:
1. Be transparent about what you're really working on. "I'd like us to do this because it will solve this problem I have." That answers the question of what's the hook. He or she is going to know you're not just trying to help out, so let them know right up front what your motive is.
2. Do your homework. Know enough about things to know how your idea is going to affect his or her work or people. If you can point out the impacts yourself, along with possible mitigation or sufficient pay-back, those arguments are less likely to become obstacles. Plus you'll seem to care.
3. Do more than your share of the work. Never give them a way to say, "This is costing me more than it costs you."
4. Give him or her the credit. "Boss, look what they did to help me fix this problem." Everone involved will know the truth, but credit is high-value currency in any organization so its a great way to get your peer to see it as a win.
These steps will be effective in direct relationship to the reputation you already have for integrity. If you've earned a shady name, good luck getting any cooperation from your peers. If your personal brand is strong, some will follow just hoping a little bit of whatever you have will rub off on them.