First step is to migrate all users to the Active Directory, mainly this means that you will have to rename their accounts in order to match their AD login (“sAMAccount” attribute on LDAP).
With groups it’s harder because unless your company is really tiny, you may not want to map all groups. The solution that I came out with is create an Exchange mailing list named “jira—mapped-groups” and to add the group that you want to see in Jira to it.
Also you can create another mailing list named “jira-virtual-users”. To this mailing list add other mailing lists or groups from your directory, the ones that you want to appear as users in Jira. This will allow you to assign tickets to these virtual-users, which can be group-roles like “Defect Coordinator”, or just teams.
You need to be aware of the fact that these virtual users will never be able to login to Jira, but they do not have to. Each real user would use his account to access jira, and if needed they can claim the tickets that were assigned to the virtual user.
This address a big limitation in Jira, the inability to assign tickets to more than a person.