Many people have both a personal and a professional presence on Google+. They have a regular Google account and profile and a Google Apps account and associated profile. The challenge is one of discovery. You have two profiles but would like your main one to be more easily discovered than the other one. In this case your Google Apps profile over your regular Google profile. While it isn't possible to hide your regular profile completely it is possible to de-emphasize it. This is the approach explained below. It makes sense that a profile with very little detail and no activity is less likely to be indexed higher than an active account with lots of detail of the same name.
Naturally, in addition to de-emphasizing your regular Google profile you need to also promote your Google Apps profile.
Start by going to the Google+ profile of your regular Google account. This is located near the top of the pop out menu on the left side of the desktop browser version of Google+. Just under home. There are nine sections in your profile. Clicking on the edit link at the bottom of each section will allow you to change the settings.
People
Under "In Your Circles"- Uncheck the box "Show people in..."
- Set "Who can see this? to "Your circles"
Under "Have you in circles" uncheck the box "Show people who have added you to circles"
Work
Change all settings to "Only you" and remove any details.
Places
Change all settings to "Only you" and remove any details.
Contact Information
Change all settings to "Only you" and remove any details.
Apps with Google+ Sign-in
Uncheck the box "Show this card on your Google+ profile"
Story
- Delete anything you have written in "Tagline"
- Under "Introduction" section add "Follow me here" with a link to your Google Apps Google+ Profile.
- Set "Bragging rights" to "Only you"
Education
Change all settings to "Only you" and remove any details.
Basic Information
Change all settings to "Only you" and remove any details.
Links
Change all settings to "Only you" and remove any details.
Your Circles
You might want to empty you circles completely. This depends on how many people you have in them. It might be helpful to share your current circles from your regular Google profile with your Google Apps profile first before you delete them.
Cover Photo
If you are graphically inclined you might want to create a cover graphic with some text in it asking people to follow you on your professional profile. Otherwise you might just want to change to one of the canned cover photos Google provides. The overall impression you are trying to create is "nobody is home here".
Posts
It's possible to delete your posts however this can only be done one post at a time. It could be quite time consuming to delete all your posts so maybe just a month or two worth is enough to aid your "nobody is home here" look.
Deleting a post is a simple as hovering over the post and selecting "Delete post" from the dropdown that appears in the top right corner of the post.
Settings
The last change you need to make, and one that will possibly make the biggest difference, is in your Google+ settings.
Google+ settings are located at the bottom of the pop out menu on the left side of the desktop browser version of Google+. Scroll down to the profile section and uncheck all the boxes in the section. In particular "Help others discover my profile in search results".
That's it. If you have any changes or additions feel free to put them in the comments.