In this tutorial, we will show you how to install TWRP custom recovery on your Xperia Z3 without locked bootloader. However, this tutorial required a rooted Xperia Z3 (read here to know how to root Xperia Z3 with locked bootloader). Custom recovery provides a number of advanced features over and above the stock recovery, such as Nandroid (system dump) backup.
How to install TWRP Recovery on Xperia Z3 with locked bootloader
- Install a root file explorer like ES File Explorer on your phone and mount /system rw. 
- Download Z3 Dual recovery [HERE] on your computer and extract the zip file (courtesy to XDA). 
- Connect your Z3 to your PC via USB cable and double click install.bat (from your extracted folder). 
- Choose option 1 and follow the on screen instructions. The phone will test reboot to TWRP recovery. 
- Reboot your phone and you are good to go. Congratulations, you have been successful to install TWRP on Xperia Z3. You will see a new application NDR Utils installed on your Xperia Z3, which helps you boot your phone to the chosen recovery (source – XDA)