>I have introduced a new feature to my site in which members can submit posts
So they can do that now?
>I would like members to be able to author posts as well.
So they can’t do that yet?
Or they can, but the author is listed as ‘irieside’ ?
If the latter, then the issue is how the posts are saved.
You need to adjust the code so that it saves the logged-in-user as author.
And that is not a BP issue, but a WP code issue.