I know that the "s" becomes "z" when it comes after a voiced sound. And it is pronounced as "s" when it comes after a voiceless sound. I also know rules about possessives but I don't know how natives pronounce a word when it ends in S and "apostrophe S" is added to it.
For example: "Stannis's army".
Do you add another syllable to it? Like Stannisiz? or just Stannis and ignore the possessive S?
I really have difficulty in pronouncing words that end in S and possessive S is attached to it.
Yes, an extra syllable is added to its pronunciation, so it's pronounced Stannisiz ([stænəsɪz]*).
Whenever a word ends in a sibilant or an affricate and you add the 's to it, the 's is pronounced [ɪz]. The pronunciation without the extra syllable is also common.
I have explained why add an extra syllable for the 's in another answer to a question asking Why are there three pronunciations for the plural “-s”?, I'll just copy-paste the relevant bit:
When a word ends in a sibilant [ʃ], it's voiceless and when we add the [s] then we get *[ʃs] cluster, which isn't permissible, so we insert a vowel between both the sibilants in order to break that cluster and conform with the rules. After inserting the vowel, we get [ʃɪs], now we already said that the -s is [z] after a voiced sound, and the vowel is voiced, so we change the [s] back to a [z] and get [ɪz] therefore the word bushes is pronounced bush[ɪz]. When a word ends in [ʒ], we do the same as above.
[s] and [z] are sibilants, but I'm going to explain them separately. When a word ends in a [s], it's a voiceless sound, so we add the [s] form of the -s ending; bus + [s] → *[bʌss], here we have a geminated s and as we read in the rules that tautosyllabic geminates aren't allowed, therefore we insert an epenthetic vowel [ɪ ~ ə] to break the geminate: [bʌsɪs], we change the terminal [s] back to a [z] because the sound preceding is a voiced (vowels are always voiced): [ˈbʌsɪz].
The same goes for words that end with a [z]: when a word ends in a [z], it's voiced so we add the [z] form of the -s ending: rose + [z] → *[ɹəʊzz], here we have a geminated z, so we need to break it, therefore we insert a vowel: [ˈɹəʊzɪz]
Affricates—[t͡ʃ] and [d͡ʒ]—are complex segments. The second segment in both the affricates is a sibilant. So we get Sibilant + Sibilant, which isn't allowed. Therefore we insert a vowel between the affricate and the [s] or [z] to break that cluster. Beach + [s] → *[biːt͡ʃs] + [ɪ ~ ə] → [biːt͡ʃɪs]
It holds true for possessives and present singular -s too.
