Learn Turkish: Gelecek yıl terfi ediyormuş, bu yüzden şimdi zam istemiyormuş. - I heard she is getting promoted next year, that's why she is not asking for a raise now.

The suffix -yormuş combines the present continuous -iyor with the hearsay/inferential suffix -muş. In terfi ediyormuş and istemiyormuş, it translates to 'I heard she is [doing]' or 'Apparently she is [doing]'. It shows you learned this information from someone else, rather than witnessing it yourself.

Why do we use the present continuous -iyor in terfi ediyormuş when the sentence starts with Gelecek yıl (next year)?

Just like in English ('She is getting promoted next year'), Turkish frequently uses the present continuous tense for planned future events. Adding -muş simply adds the 'I heard' aspect to that planned future action.

Why is the negative verb istemiyormuş spelled with an 'i' instead of an 'e'?

This is a great refresher on vowel narrowing. The verb is istemek and the negative suffix is -me. However, the -y in the continuous suffix -yor 'narrows' a preceding -a or -e into an -ı, -i, -u, or -ü. So, iste-me-yor-muş correctly becomes istemiyormuş.

Why does the t in terfi etmek change to a d in terfi ediyormuş?