Is there a way to have trash email folder automatically empty itself after a week?

This is not possible with the Mail app for the iPad. Furthermore, You can suggest this feature directly to Apple by leaving a product feedback here 👉Product Feedback - Apple 

Axel F.

Hi GatorJoe0216, thank you for posting in Apple Support Communities.

In addition to the above linked article please also look at the below linked article as for an iCloud email account you can set deleted messages to be removed after:

1. after one day
2. after one week
3. after one month

Although this only affects iCloud emails.

Other emails accounts are subject to the account but again the following linked article explains this further:

https://support.apple.com/en-au/guide/ipad/ipad0bf80ff4/ipados

You can also contact Apple Support as follows:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above but also again as follows Apple – Location Selector; or
• Using the "Apple Support" app, available and downloadable from App Store.