Sim may need activating.
If you could just double check it's been placed correctly, our sim cards are triple sims which means they are standard (Large) Micro Sim (Medium) and Nano Sim (Small). Xperia usually takes Nano.
If it has been placed correctly it might mean the sim card is not activated yet you can ring 202 to get this activated.
This also could happen if there was a fault with the handset or incompatibility, for example, a third party network phone unlocked. If this is not the case give 202 a ring on an O2 a mobile in contract 4445 if on Pay & Go and see if it's activated.