Hi there
Most SMART tv's allow you to connect a hard drive to the TV (usually via a USB socket) to enable you to both pause and record programmes.The instructions will show you if this is available on your set and how to do it. Does the remote have a pause TV button on it ? If so what happens if you press it whilst watching a show ?.
The YouView element alone allows you to connect to the relevant catch up channel and play the show seamlessly from the EPG for the shows you may have missed over the past few days.
If you tell me the make and model I will try and find out if this feature is available for you.