食べた後で…

When あと(後)is modified by a past-tense verb, it becomes a time expression that shows what happens after the action of the verb is completed.

食べた後
After we’ve eaten

When the above time expression is used with the particle で , it can be used to say when another verb happens.

食べた後で映画館へ行きましょう。
After we’ve eaten, let’s go to the cinema.