Focus on the word "Despite". It says that despite having engineered and overseen the return of several unexpected and things out of place under his predecessor's negligence or laxity, still the bishop had a modest and open quality that belied/failed to justify the emininence of his position.

whys the hint for belied?

Someone please explain why derided is wrong

In a nutshell, the meaning of the sentence is this:

Even though the previous vicarious was not good (laxity or negligence), the new one disproved (belied) who thought the new course would be much positive. Indeed, the ongoing action is pretty much the same the previous. In addition, considering the powerful position of the new bishop.

Hope this helps.

Regards

Despite having engineered and overseen the return of several stray dioceses that had broken away under his predecessor's negligence, the bishop had a modest and open quality that why not construed? the eminence of his position.
Contrast word Despite shows that there should be a positive connotation in the second sentence. Isn't so?
@carcass please help

Exactly.

Laxity, belied, eminence

kudos

I think
audacity is more correct than eminence because the later is shared between him and his predecessor

Despite having engineered and overseen the return of several stray dioceses that had broken away under his predecessor's (i)_________, the bishop had a modest and open quality that (ii)_________ the (iii)_________ of his position.

The bishop "having engineered and overseen the return of several stray diocese" is contrasted with his predecessor, who, therefore, must lack the dynamism of the current bishop, causing these stray diocese to break away. The word from the choice list is laxity.

The sentence fragment:

the bishop had a modest and open quality that (ii)_________ the (iii)_________ of his position.

is contrasted with his

having engineered and overseen the return of several stray dioceses that had broken away under his predecessor's (i) laxity

Clearly the bishop's position should be an eminent one given his achievements. The audacity of his position does not make sense in this context. Yet the bishop had a modest and open quality which belied the eminence of his position.
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To construe is to interpret a word or action in a particular way.

Only a living entity can construe. The modest and open quality cannot construe the eminence of his position.

Also, the "despite" at the beginning of the sentence contrasts his achievements with his modest and open quality. The word "despite" itself suggests "belied".
_________________

The word "Open quality", hence, belied is the correct synonym of being honest
Hope this helps.