Connection to TV using HDMI to lightning adapter

If you already tried (to no avail):

• A reboot of your iPad and your TV
• A different HDMI port on your TV
• A different HDMI-HDMI cable

it might be a defective adapter, and/or your iPad's port defective.

I suggest that you make an appointment (*) and have your device + adapter inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> Apple – Location Selector. After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.