Syllables

The way I say it, four.

Four for me, too, because 'headmaster' is a noun. Pronouns subsume the extra syllable: I'd, you'd, we'd, etc.

But a native speaker tells me that there are only three syllables in the word "headmaster'd."

sitifanBut a native speaker tells me that there are only three syllables in the word "headmaster'd."

For a few, that could be true, but I suspect that they are actually not listening closely to themselves.

I have consulted Longman Pronunciation Dictionary, there are only two syllables in the word mastered.
head (one syllable) + mastered(two syllables) = three syllables
How come there are four syllables in headmaster'd?

sitifanHow come there are four syllables in headmaster'd?

Because the "-'d" represents 'had'. It is not normally pronounced the same way as the regular past ending "-ed" when attached to nouns...unless the noun ends in a vowel sound.