In a way that allows or enables connection; in a manner that permits joining or linking.
From 'connectible' plus the adverb suffix '-ly', creating an adverb form that describes how something can be done in a connecting way.
This is an extraordinarily rare adverb that you'll almost never encounter in actual usage—it's a 'theoretical' word that exists because English rules allow it, even though speakers rarely feel the need to use it.
Complete word intelligence in one call. Free tier — 50 lookups/day.