There is no one-size-fits-all answer to this. You’ll have to ask yourself where the user is more likely to look, which will often be little more than guesswork.
There are a few very basic rules of thumb, but you still need to use common sense before applying them:
Users (at least those who have experience using dictionaries) are generally speaking more likely to look under the head word: for ‘religious war’, they’d be more likely to look under war, and for ‘prime minister’, they’d be more likely to look under minister.
If one of the elements is a particularly common word (like give in ‘give a speech’), and the other is less common (like speech), it is often better to put it under the less common word, since entries like give tend to be very long already, and examples are easy to miss in very long entries.
If the entry is a very tightly-knit compound, it is sometimes a good idea to include the compound as a separate entry; many English-language dictionaries include prime minister as an entry, for example.
Of course, you also have to remember that bilingual dictionaries have two major groups of users: speakers of the source language learning the target language, and speakers of the target language learning the source language. Members of these two groups may not look the same place for the same thing.
Let’s say your dictionary is English–Warlpiri as an example.
A native English speaker looking for the Warlpiri word for ‘prime minister’ will likely either look directly for the compound as an entry or look under minister. I would not expect an English speaker to look under prime except as a last resort.
A Warlpiri speaker who comes across the term and already knows what minister means (but not what prime means) will likely first look under prime, since that’s the word they don’t understand. If the compound is not listed there and they can’t guess the meaning from the combination of prime and minister separately, they will likely also look under minister under the assumption that a prime minister must be a type of minister. If they know what prime means (but not minister), they will obviously most likely do it the other way around, with minister first and prime second if necessary.
A Warlpiri speaker who knows neither word will likely look them up in the order they appear in the text; they will find the compound wherever it’s listed, but faster if it’s listed under prime.
In a case like this, my advice would be to include the compound under both entries. Cross references from one entry to the other are also useful, especially if the translation is not simple and straightforward.
