Pat chicken dry, rub with olive oil, salt, and pepper; tuck lemon halves and rosemary into cavity.
Set Instant Pot to Sauté; brown chicken 3–4 minutes per side until skin is golden.
Remove chicken briefly, pour in broth and scrape browned bits. Place trivet in pot and set chicken on trivet breast-side up.
Seal lid and cook on Manual/High for 6 minutes per pound (about 20–24 minutes for 3–4 lb). Natural release 10 minutes, then quick release remaining pressure.
(Optional) Roast under broiler 3–5 minutes to crisp skin if desired. Let rest 10 minutes before carving.