Rarely, though, do countries introduce a single reform alone.
What function does do have in this sentence?
This is an example of inversion.
In formal styles, when a "negative" adverb (such as "rarely" or "never") is used in the front position (for emphasis) the subject and verb are inverted.
Never have I been so surprised. (= I have never been so surprised)
When the verb is in the simple present, "do support" is needed to form the inversion
Rarely do I wake before 7am.
Seldom does one hear the howl of a wolf.
Your sentence means the same as
Countries rarely introduce a single reform alone.
In implies that countries usually introduce multiple reforms at the same time.
One thing it does is allow the writer to emphasize the word 'rarely'. My guess is that this sentence exists in a larger context where the action of introducing a single reform alone is being compared to another action that happens more often. Instead of writing
"Countries rarely introduce a single reform alone, though."
the writer wants to increase the importance of the word 'rarely' by putting it at the beginning of the sentence. The word 'do' is needed as an auxiliary because the main verb must come after the subject in this case. In English, you can't write
"Rarely, though, introduce countries a single reform alone."