Hi Sharat,
You can achieve this by configuring the ACL settings for the user group.
In the ACL>userGroup>Compose setting of the user group, configure these two settings:
'Allowed To Write New Post' > Yes
'Allowed To Publish Post' > No
http://take.ms/4CbtZ

The user group should be able to make a new post but would require approval beforehand by admin. Hope this helps.

Hello and thank you for the reply. Did the same, but the "Quick Post Module" does not show any option for the public to post.

Thanks,

Sharat

Hey Sharat,
The quick post module follows the ACL configuration of those two options I mentioned to you. Perhaps you can check the user belongs to which 'usergroup'. Then check the ACL setting for that 'usergroup'. If you are still having issues, perhaps you can provide us backend access to your site so we can help you check.