Let's divide the verse into two parts:
נשאו נהרות ה'—נשאו נהרות קולם
ישאו נהרות דכים
Each part is one sentence.
The first one is broken up poetically by a caesura, around which both the subject and verb are repeated. So the reason "נשאו" and "נהרות" are identical in each of their appearances is simply that they are repetitions of the same word....
There are a few answers given to this question.
@Alex noted the Rav Pealim (hebrewbooks, sefaria), who suggests that the vav-verse is missing, to show that it was not written on the 6 days of the week.
This paper (end of page 3) cites a number of earlier sources that note that when one letter from the beginning is removed, and a final line beginning with פ ...
As a more homiletical than exegetical discourse, this question is presented in the Midrash on Tehilim (ch. 100). IMHO, the fundamental reconciliation is simply that both happiness/joy and fear [of God] should be exercised in one’s service of God.