Eg : αὐλέω to αὐλητής, actually. 🙂
For a list of suffixes and how they work in Ancient Greek, see Herbert Weir Smyth, A Greek Grammar for Colleges from §833 on for more detail than you’ll ever want on the mechanics. The list starts at §839.
That list is for Ancient Greek; Koine is substantially the same list, and works the same way, but some suffixes did fall out of fashion. For example, -τήρ is Attic, -τής is Attic and Koine.
For accentuation: the rule in Koine remains the rule for Ancient Greek: accent is governed by Mora (linguistics). (It’s terrifying how strongly the rule applies, by analogy, even after vowel length was eliminated in Greek, as it was by the time of the New Testament—and indeed, even in Modern Greek, two millennia later.)
By default, accent is recessive. So if the suffix is unaccented, and ends in a long syllable, then accent will be on the penult. If the suffix is unaccented, and ends in a short syllable, then accent will be on the antepenult. So σημαίνω > σημάν-τωρ; μανθάνω > μαθή-τρια.
Many suffixes bear accent, and that accent overrides the recessive default. αὐλη-τής is one such instance: the agentive -τής is consistently accented.
The only instance where accent makes a meaning distinction is one familiar to students of the Koine from the Paraclete. If you form an adjective in -τος from a prepositional verb, there is meant to be a meaning difference between accenting on the ultima and the antepenult. Accenting on the ultima means the description in the adjective applies as a one-off. Accenting on the antepenult means the description in the adjective applies permanently.
So a παρακλητός is someone you’ve summoned to stand by your side just now. A παράκλητος is someone you summon all the time, a permanent advocate. Which is what the Holy Spirit is supposed to be.
(Given that the instance of παράκλητος in Dio Cassius 46.20 refers to slaves dragooned into a one-off task, that accent distinction turns out to be bogus in practice, and I’ve seen oodles of other instances where it was ignored. Sorry.)