Learn Dutch: Na te zijn geslaagd, hoeven we niet meer te oefenen. - After having passed, we do not need to practice anymore.

The verb slagen (to pass/succeed) uses zijn as its auxiliary verb in the perfect tense (for example, wij zijn geslaagd). When you build a perfect infinitive clause with na ... te (after having...), you must stick to the same auxiliary verb the main verb normally uses.

Could I change the word order to Na geslaagd te zijn?

Yes, both word orders are perfectly fine! In these perfect infinitive clauses, you can place the past participle (geslaagd) either right after na te zijn/hebben, or at the very end of the clause.

Why does the second half of the sentence begin with hoeven instead of we?

This is because of the Dutch V2 (verb-second) rule. The entire first clause (Na te zijn geslaagd) counts as the first position in the sentence. To keep the main verb in the second position, hoeven and the subject we swap places (inversion).

Why is hoeven used here instead of moeten for "need to"?

In Dutch, when you want to say you "do not have to" or "don't need to", you use hoeven plus a negative word like niet. You cannot use moeten niet for this, because that means "must not" (a strict rule). Remember that hoeven always teams up with te before the other verb (here: te oefenen).