If there's a substantial waiting time in the onboarding process between requesting access and receiving it, then no. It will be impossible to keep them active. The user has 0 incentive to use the app at this point, simply because he cannot do anything anyway. Some ways to relieve this frustration:
Making it really clear that the user needs to wait for the admin to confirm access for him, but it's totally worth the wait.
How effective this works depends on whether you are able to leverage the waiting time into a positive experience. This can be done by simply communicating the app's benefits so well that the user is willing to wait, or even better - starts to anticipate using your product. Some services use the principle of exclusivity to make the waiting time rewarding. Think Dribble - you need to be invited to use it properly, but you can put yourself on a waiting list and wait for a random invite. People will be willing to wait if the benefit of using it outweighs the cost of waiting. If you know how long it takes before a user is accepted, you can add things like countdown or something similar. Many video games do this before their release.
Make it really easy to step back in where you left off in the onboarding process.
If a user receives a message that they've been accepted, make it really easy to go from there back into the app. The use of the endowed progress effect may be applicable here for you. Show any steps that may have preceded the point where the user was forced to wait. Then the chance is higher they will stick to their previous commitment to start using the app.
Keeping the user active is likely impossible. Keeping them interested is not. Doing some user research to figure out what works and doesn't to keep your target audience engaged is your first step.