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Do you use simple past + simple past/past perfect?
Example: She ate before they had arrived.
She ate before they arrived.
Or Simple past + present perfect?
She ate before they have arrived.

If you can explain tenses that should follow each others that would be great. Like simple past can only be followed by simple past or past perfect, etc.
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Mercyful_fateShe ate before they had arrived.
She ate before they arrived.
If X is before Y, then X is farther back in time than Y. The past perfect is farther back in time than the simple past. So this shows the time order best:

She had (already) eaten before they arrived.
_______

Nevertheless, the word before is enough to show the time order, so you can simplify thus:

She ate before they arrived.
_______

(Your other example with have arrived is not correct.)

CJ
Comments  
Generally, you are supposed to keep a sentence in the same time tense. Simple past + present perfect is ungrammatical in your example.
Each combination has a purpose. Simple past + past perfect is used to indicate that the past perfect action happened first.
If you have a list of usages for each tense, that should give you an idea of how to use combinations.
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Thank you. Can you help me please in finding the list of usages for each tense?
 CalifJim's reply was promoted to an answer.