I'd say that depends on how far away the intelligent life in question is. Are they close enough that we can communicate with them? Are they close enough that they might try to invade Earth? In that case, the military would get involved. However, if they're thousands of light years away and they, like us, have no means of traveling faster than light, then we'd just try to study them.
NASA wants to protect other planets in our solar system from contamination with earth life - this is called:
It's not clear what would be done if we found intelligent life. SETI - Search for ExtraTerrestrial Intelligence - is an institute that is, or was, trying to do that:
Here's what Wikipedia says:
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