Rinse and drain the olives and capers, then pat them dry with a towel.
Pulse garlic, anchovy paste, capers, and lemon zest in a food processor until finely chopped.
Add kalamata and green olives with the parsley. Pulse in short bursts to a coarse chop.
Drizzle in olive oil and lemon juice. Pulse just until combined, scraping the bowl once.
Season with red pepper flakes and black pepper. Pulse once or twice to mix.
Let the tapenade rest 10 minutes to meld flavors, then serve or chill.