Is that a Mazda? Looks familiar.
Anyway, you have a number of options here. The simplest one is to order a replacement door card. This might sound expensive but if you scour the breakers yards and online auction websites you may find one cheaply.
Alternatively you can remove the door card and then, working from the rear of the panel, remove the fabric and then use a spray adhesive to affix the fabric back to the panel.
Another option that may yield some success is to leave the door car on the door but remove the plastic insert that's in the middle of the fabric (with the electric window switch in it) which will let you get underneath the fabric to apply some spray adhesive to the back of the fabric.
Your final option is to remove the panel and give it to a specialist furniture upholsterer or vehicle trimmer.
If you feel particularly flush, you could find a complete leather interior with seats and door cars and change the lot. This is obviously a bit of overkill but would be worth considering if a second hand interior can be had for a good price.