In the bottom of a medium-size mixing bowl, make the dressing by whisking together the olive oil, lemon juice, garlic, anchovy, dijon mustard and a few cracks of black pepper.
Add the drained tuna to the dressing and use a fork to break the tuna into small pieces. Toss it to coat well in the dressing. Stir in the celery, olives, red onion, parsley and basil. Taste and add more black pepper and salt if desired. Serve on its own, with crackers or in a sandwich.