Green 02 is a properly warm green, and it wants warmth around it. The trick is to lean into that and avoid anything that fights it.
For woodwork and trim, go for a chalky warm off-white rather than a brilliant white — a brilliant white will look stark and clinical against it. Paper III from Paint & Paper Library (LRV 75.3) is a lovely soft option, or Au Lait from Farrow & Ball (LRV 80) if you want something with a creamy, milky warmth that picks up the green's natural softness. Both keep the scheme calm and let the green do the talking.
Then bring in your accents. This is where Green 02 really comes alive. Cigar BH.20 from Mylands (LRV 11.8) is a deep, smoky oxblood-leaning brown that grounds the whole room — gorgeous on a chimney breast, a piece of joinery, or even a single panelled wall. For something punchier, Fuchsia Falls 2 from Dulux (LRV 29.8) gives you a bold, jewel-toned accent that flatters the green without clashing — think a single chair, a cushion, or art.
Textiles are your friend here. Oatmeal linens, clay-coloured wools, and anything in the natural tan-to-terracotta range will sit beautifully against the green. Metalwork should be antique brass — not chrome, not brushed nickel. Brass picks up the warmth; cooler metals deaden it.
The one thing to avoid: cooler blue-greys. Pair Green 02 with a Pavilion Gray or similar and it goes flat and a bit muddy — the warmth gets cancelled out and the whole thing falls a bit lifeless.
My advice — paint a large board with Green 02, prop it against your chosen off-white trim, then drape your actual textiles over it. Live with it across a day. Warm greens shift a lot between morning and evening light, so you want to be sure your accents still read right after dark.