Sebastiano Massimo Giuseppe Barbagallo 

I'm afraid a transfer of an installed program from one PC to another is not possible, at least not in a Windows environment. Your new PC may have the same operating system, but will certainly have different components, so even trying to install an image of your old PC in the new PC will most probably cause a lot of trouble and never work properly.

As SDL Trados Studio 2011 is not supported anymore and is really fully outdated in terms of functionality, the best option would be to invest in Trados Studio 2024. TS2011 has been developed 14 years ago, which is ages in terms of software development.

Sebastiano Massimo Giuseppe Barbagallo 

In addition to what Jerzy said, let me tell you that Studio 2011 has reached end of life, which means that even if you make a fresh installation on your new PC, you will not be able to activate the software. 
More details on this can be found in this KB article:
End of Life Information for Trados 2007, Trados Studio 2009, 2011 and 2014 License Resets and Installation

Thank you for your answer. Do you think that if I try to transfer the hard disk containing Trados Studio 2011 on a new PC almost identical to the old one (same operating system et cetera) I would risk losing my license forever?

Thank you for your answer. Do you think that if I try to transfer the hard disk containing Trados Studio 2011 on a new PC almost identical to the old one (same operating system et cetera) I would risk losing my license forever?

Sebastiano Massimo Giuseppe Barbagallo 

If you just mean installing the HDD from your old PC in your new PC, this will never work. You will have files and folders there, but NO software installed on your old PC will ever work in your new PC. You will be able to access all files and folders, though, so your projects possibly existing there will be still accessible.

You have to install all your software on your new PC anew. There is no way around it. And Windows does not have any migration tools from what I know.

Sebastiano Massimo Giuseppe Barbagallo 

Very risky.  You may be better to leave it running on the existing PC or explore upgrading to a supported version of Trados Studio to ensure smooth operation on newer hardware as Jerzy and Walter suggested.

If you're looking for some sort of technical reason... and I cannot be 100% on this and can't test anyway since Flexnet has been completely decommissioned... but I think that FlexNet generates a unique hardware fingerprint based on components like your motherboard, CPU, and hard drive.  When you transfer your hard disk to a new machine, even if the operating system remains the same, the hardware changes will result in a different fingerprint.  FlexNet will detect this as a different machine and could treat it as a new activation request, which it cannot process without support.