It's quite clear that your question is from an exercise in a grammar book or something similar. (And thus, the context is the exercise.)
Hence, the expected answer would be (4) has been running.
The following entry in Practical English Usage by Michael Swan should make this point clear:
458.6 actions and situations that have just stopped
We also use the present perfect progressive for actions and situations which have just stopped, but which have present results.
You look hot. ~ Yes, I've been running.
Sorry I'm late. Have you been waiting long?
I must just go and wash. I've been gardening.
Also note that has been running is likely the expected answer because the exercise includes the first sentence: She is exhausted, which is in the simple present (the verb is be; and exhausted is an adjective), and is a hint that the exercise expects you to relate the two sentences. (So, it's like "She's exhausted. Why is she exhausted?" "Because she has been running.") Keep in mind that in real speech, it's not impossible that a native speaker may use other choices (e.g., She's exhausted. She was running.) as you can see in several comments here. -- Another important point, as @Mari-Lou A mentioned in her comment under this answer, is that if the first sentence were in the simple past (i.e., She was running), shifting the tense of has to had would have been more appropriate, and She had been running would have been a better answer.