How can I check if there's element in my arraylist that is not in the hashmap?

Given that your condition is

if there's any element in my List that is not in the Hashmap

you can use anyMatch while iterating over the list of elements to check if any of them is not present in the hashmap values.

return someStrings.stream().anyMatch(val -> !myHashMap.containsValue(val))

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Or to look at it as if all elements of someStrings are present in hashmap values

return someStrings.stream().allMatch(myHashMap::containsValue);

A similar check though could also be using containsAll over the Collection of values :

return myHashMap.values().containsAll(someStrings);

No need for streams, you can just use the good old Collection#removeAll():

Set<String> copy = new HashSet<>(someStrings);
copy.removeAll(myHashMap.values());

Now copy will contain all the values not contained in myHashMap. You can then do something with them (like iterating) or just call Collection#isEmpty() to check if all are contained in the map