Yes, very easy. Check in the settings at what your recording settings are. I think recording the last 30 ish minutes is the max, then simply press the share button directly after the gameplay footage you'd like to have saved. PlayStation has an app called ShareFactory where you can edit all your recorded gameplay directly on the console.
Or
You can double tap the share button and it starts recording immediately (Which means you can record as you play)
Once you are playing, you can start recording at any time by double tapping the share button. Once you want to finish your recording, simply double tap the share button again.
So there are two ways to record.
1. A single press of the share button to record what you just did.
2. A double tap of the share button records as you go.