So my workplace had just recently upgrade my Mac Pro to iMac.
I was using Adobe CS4 and similarly got upgraded to Adobe Creative Cloud on my new iMac
When I took over the job from the previous motion graphic artist, all the third party plugins are already installed and running.
Therefore I am totally clueless how to go about transferring/installing everything from my old desktop to my new iMac.
The 3rd party plugin I wish to transfer are the Trapcode suite
There's nothing to transfer. You have to buy the upgrade from Red Giant Software and install it. CS4 was 32bit only and all current versions are 64bit, so for that reason alone it wouldn't work, not to speak of specific CC 2015 requirements necessitating upgrades. The same would apply to pretty much any other third-party stuff.