How can I buy an app from the App Store and download it to my wife's iPad?
Gift an item on an iOS device


Find the item in the App store or iTunes store that you wish to gift.
Tap the Share icon in the upper right. 
Tap the Gift icon.
Sign in to the iTunes Store with your Apple ID.
Type the email address for the person you want to send the iTunes Gift to. 
If you want to, add a message.
Pick the day you want to send the gift.
Select a theme for your gift.
Tap Buy, then tap Buy to confirm.


Gift an item on Mac or PC


Sign in to the iTunes Store with your Apple ID.
Find the item in the App Store or iTunes Store that you wish to gift.
Click the arrow to the right of the price and select Gift This. 
Type the email address for the person you want to send the iTunes Gift to.
If you want to, add a message.
Pick the day you want to send the gift and click Next. 
Select a theme for your gift and click Next.
Confirm your gift purchase and click Buy Gift.


Ref: https://support.apple.com/en-us/HT201783