I don’t know how such a useful word has alluded me for all these years. The word obstante did not come onto my vocabulary radar until recently (after having been a Spanish speaker for 7 years). However, the word obstante is a very useful one.
As a conjunction it can be expressed with the basic English word but. There are many other words that can be translated as obstante: however, nevertheless, nonetheless, albeit and notwithstanding.
As an adverb obstante can be use as in spite of or despite.
There are other Spanish word which may map more exactly to the words listed above, but this list gives you a broad sense of what obstante is trying to express.