The answer to your question would be that the verb or verb phrase that completes the sentence without shifting tenses unnecessarily is the following one: Was. That is, the sentence would be as follows: Immediately after I played tennis with Mara yesterday, I was exhausted.
The verb tense used in this passage is the past simple. The past simple tense, also called the simple past, is used for past actions that happened either at a specific time, which can be given by a time phrase or understood from the context. In this case, the time phrase indicating that the action started and ended at a speficic time is "yesterday".