You need to get the car's immobiliser programmed to accept the new ID40 transponder chip in the key. This requires Tech-2 or other suitable software and interface, you will also need the PIN code from the car pass. If the key has a remote fob then that will need similar programming so that it can arm/disarm the alarm where fitted, and to operate the central locking. AIUI you can't sync the remote unless it's first registered with the car. Also the remote transmitter fob circuit is different between factory fit alarm and no alarm models so make sure you get the correct one. I've never come across an Omega without a factory fit alarm but apparently they exist.
The same system was used on other Vauxhall cars of similar vintage so it's not unique to Omegas. Hence I would expect that any competent auto locksmith should be able to cut your new blank key and program the car. Might be pricey if you do it as a call-out. so phone around and take the car to them.
Some of the OOF members have Tech-2 and might help you out for a small fee.
AIUI cloning is not recommended.