Nencia is the aunt of the old man's grandmother and works under the Duchess and seems to be trusted greatly by her. The trust seems well founded as Nencia does not pass on the Duchess's information or secrets: she "was mute as a fish where her lady was concerned"[1] and never changes in this regard either. Between the lines, it seems that Nencia may have more information concerning the Duchess's 'intense prayer sessions' in the chapel[2]. This assumption is supported by the fact that Nencia is tasked with warning the Duchess if others (mainly the chaplain) approach while she is revering the relics (which seems to be a euphemism for amusing herself with Ascanio below).
As to her character, Nencia seems to be endowed with both good common sense and a keen eye for her lady's behavior. There are multiple instances that demonstrate this. Such as Nencia feeling that though the Duchess, upon trading her customary gowns for more subdued clothes, "looked the lovelier for the change" she thus "gave the Duke greater displeasure."[3] A second example is when Nencia is quite aware of the consequences of the Duchess's careless rebuttal of the chaplain's request for book allowance but says nothing due to her position and the Duchess's nature: "Now Nencia always had it in mind that her grace had made a mistake in refusing that request of the chaplain’s; but she said nothing, for to talk reason to the Duchess was of no more use than praying for rain in a drought."
[1] Wharton 1901, p. 7
[2] see Wharton 1901, p. 11
[3] Wharton 1901, p. 9