A verb "PROtest" with stress on the first syllable exists, meaning more or less "participate in a PROtest", and derived from the noun, which has first-syllable stress.

"Protester" can have stress on either the second or first syllable, depending on whether the speaker thinks of it as being formed from the verb "proTEST" with second-syllable stress or from the verb "PROtest" with first-syllable stress. This topic is covered in the 2011 Language Log post "[Protesters][1]", by Eric Baković.

The comments on that page have some useful additional information, such as this:

> in his pronunciation dictionary, John Wells gives both options for the verb in both BrE and AmE.
>
But more interestingly, under *protester,* he gives the results of one of his pronunciation polls, albeit for BrE only:
>
*Preference poll, British English: [stress on the second syllable] 69%; [stress on the first syllable] 31% (born since 1982: 45%)*
>
>Note that the polls were done on paper, via regular mail (!), and – if I remember correctly – essentially on a self-report volunteer basis. So any "new" trends may be underreported. Or overreported ;)

–Jarek Weckwerth, February 21, 2011 @ 6:34 pm

  [1]: https://languagelog.ldc.upenn.edu/nll/?p=2982