Would zirconia crown fill my gap between the teeth? (photo)

You can absolutely close the gaps in your teeth without braces. Zirconia crowns would not be my first choice-  as they are not the most esthetic material available.  You also may not need crowns. This correction can be made with veneers. It would be much more conservative to your natural teeth while still solving your problem.

you can go with the crown for space closure. but the best option is space closure by orthodontic treatment. Crowns sometimes may look big and bulky.

I would recommend orthodontic treatment to address the deep bite and close the gap without removing any tooth structure. Crowns or bonding are an option. But you have to take into consideration the deep bite. Any restorations you have placed are more likely to fail if the bite is not addressed first.