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Should it be pronounced as /z/ or /s/ ?
It's is pronounced like the z in zebra.
When have means "to be obligated or forced to do X", the pronunciation can change. The v in have can be pronounced like the f in fly, and the s in has can be pronounced like the s in sand.
It should be pronounced /z/.
Normally when an "s" initiates a word or syllable, it is pronounced /s/, and when the word or syllable ends in "s" it is pronounced as /z/.