You have three issues here:
1 - Connection: If the older drive is IDE, your new motherboard may have only SATA connections. If so, you will need adapters -- both power and data -- to connect to the new motherboard. The adapters are readily available online.
2 - Drivers: When the Win7 drive boots up, it will search for necessary drivers for the new motherboard. You need to direct this search to the drivers that came with the new board -- could be CD or USB storage. If you are connected to the internet, it will search there. It may boot up with basic defaults -- video, for example -- until you provide drivers.
3 - Activation: Your Win7 installation will need to be activated with Microsoft. It will attempt to activate when you are online. If it is an older install, that will often work first time. If not, there are extra steps for activation.
It will work. I have done it many times. If more questions, post them here.