Installing AUT using testcomplete

Pretty much, if you can record it, you can do it.  This does not necessarily mean that you would want to record it, just noting that TestComplete can do a good bit of anything you need.

That said, if you need to install with admin privileges, you should run TestComplete as an administrator so that it has the proper elevated privileges to do so.  You can then script (or record) the installation process as usual and execute.

That said... side note... the only reason why I would actually use the install wizard, etc., for installing the AUT via TestComplete is if I needed to test the install wizard part.  I find that, for simple upgrades of test builds, etc., during a development cycle, doing a file copy from the build location to the local folder usually is sufficient and a lot faster assuming that the application supports that sort of thing.

If your installer is MSI, you can use the WMI method Win32_Product.Install to install the app silently. Check the example here:
https://community.smartbear.com/t5/TestComplete-General-Discussions/Install-and-Uninstall-an-application-through-the-script/m-p/96198#M19459

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anumolu9999 wrote:
Need to install the software with admin privileges

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As Robert noted, you'll need to run TestComplete as administrator in order to perform actions as admin.