Does DHA increase the effects of clarithromycin?
You've misread the paper. Clarithromycin is metabolized in part by CYP3A, but to an active metabolite. A significant proportion of clarithromycin and its active metabolites are excreted unchanged in the kidney. Clarithromycin, and other macrolide antibiotics do inhibit CYP3A enzymes, as you noted in your answer. You can read about this in chapter 55 of Goodman &amp; Gilman's the Pharmacological Basis of Therapeutics.

We certainly worry about clarithromycin and other macrolides increasing the half-life of drugs that are primarily metabolized by CYP3A4 (again, see Goodman and Gilman). Midazolam is an example, and is what the paper you cite was about. If you give clarithromycin together with midazolam, expect the effects of midazolam to last longer. The important relationship between CYP3A induction and clarithromycin discussed in the paper is not that it reduces the effectiveness of clarithromycin, but that CYP3A induction does not overcome clarithromycin mediated CYP3A inhibition.