New MoBo will it read my HDD?

I am changing all my PC Parts but the HDD Stays, theres Win7 on it and programms and stuff.
I heard when you're changing a Motherboard the Motherboard will not read your OS or your HDD.

Can I just simply connect the HDD to the new Motherboard and it will read everything as it should or won't it?

Yes, in the BIOS you will need to select it as the boot drive.
If you are upgrading hardware you may need to remove drivers such as Nvidia Geforce drivers for a GPU example.

I heard the license of for example my Win7 won't be legit anymore.
Don't know how that can happen but I heard something this way.

The license will be fine, a new motherboard may cause it to complain.
But Luke from Linus Tech Tips had a hard drive which he used in tons of test rigs and it worked fine...