Private taxi from Venice airport

Well, for obvious reasons you should tell us if you are staying on the mainland or on the islands.
Do you need a "greet private taxi" because of a late arrival?
That makes a difference if you are staying on the Islands, during the day you can take a car to Piazzale Roma and then walk to your hotel. When it's dark, Walking up and down Venice stepped bridges with luggage in tow may ruin a marriage.

Do you mean a water taxi or a land taxi?

Staying on main land. Is for my friend who is traveling to Europe for first time and prefers someone picks her up inside airport. Is not a arrival.

To be clear, what you want is a private transfer or car service, not a taxi. I've never had a need for one in Venice, but there are quite a few listed by TripAdvisor and Viator 3rd party sites. Check their reviews first.

Just do a google search for "private car service Venice airport". Several options will appear. Blacklane has had a good reputation for many years. Would not hesitate to use them.

Where exactly is the hotel?

The hotel can probably recommend a driver-check with them first

WelcomePickUps.com is a good option