Heo debuted in 2019 through the movie ''Like the First'' (2019).<ref name="KHAN211209">{{Cite news|url=https://sports.khan.co.kr/entertainment/sk_index.html?art_id=202112091348003&sec_id=540201|title=신예 허남준 ‘설강화’ 출연|publisher=京鄉體育報|language=Korean|date=9 December 2021}}</ref> His first drama appearance was in OCN drama ''[[Missing: The Other Side]]'' (2020). Heo would go on to play supporting roles in dramas such as ''[[Snowdrop (South Korean TV series)|Snowdrop]]'' (2021); ''[[The Matchmakers (TV series)|The Matchmakers]]'' (2023); ''[[Sweet Home (TV series)|Sweet Home]]'' Season 2 and 3 (2023–2024); and ''[[The Impossible Heir]]'' (2024), as well as movies like ''[[Night in Paradise (2020 film)|Night in Paradise]]'' (2020); ''[[Double Patty]]'' (2021); and ''[[I, the Executioner (2024 film)|I, the Executioner]]'' (2024).<ref name="IDN Times"/> He was nominated for the Best New Actor Award by the [[2024 APAN Star Awards]] for his performance in ''Sweet Home''.<ref name="JN24241203">{{Cite news|url=https://www.joynews24.com/view/1789536|title=김수현·변우석·지창욱→김지원·김혜윤·김태리, APAN어워즈 후보|publisher=JoyNews24|language=Korean|date=3 December 2024}}</ref>
In 2024, Heo portrayed a cold-blooded gangster and murderer named Kim Sang-hyuk (– the eldest son of [[Kim Myung-min]]'s character Kim Kang-heon) – in ''[[Your Honor (2024 TV series)|Your Honor]]'', a role which garnered Heo increased public attention.<ref>{{cite news|title='유어 아너' 허남준 "아슬아슬한 시한폭탄 같은 느낌으로 연기"|url=https://www.yna.co.kr/view/AKR20240912174200005|language=Korean|work=Yonhap News|date=12 September 2024}}</ref><ref>{{cite news|title="'유어 아너' 허남준, 노출신 각오한 이유.."감독님, 미팅부터 근육 체크" [인터뷰 종합]".|url=https://www.chosun.com/entertainments/broadcast/2024/09/11/Q4Q24GDNRGJCFOBVUHLMKWBEKI/|language=Korean|work=Chosun Ilbo|date=11 September 2024}}</ref><ref>{{cite news|title=""너무 매력적인 나쁜 새끼"..'유어아너'가 낳은 최고의 子 허남준 [Oh!쎈 레터].|url=https://www.chosun.com/entertainments/broadcast/2024/09/21/OZQGNTCDBPDU5SVM6AHD2AKIMQ/|language=Korean|work=Chosun Ilbo|date=21 September 2024}}</ref> During that same year, Heo portrayed Ji Sang-woo, a warm-hearted psychiatrist and YouTuber who specialized in unsolved cases in ''[[When the Phone Rings]]''.<ref>{{cite news|title=Heo Nam Jun turns into a psychiatrist for ‘When The Phone Rings’|url=https://www.thestatesman.com/entertainment/heo-nam-jun-turns-into-a-psychiatrist-for-when-the-phone-rings-1503356176.html|work=The Statesman|date=21 October 2024}}</ref><ref>{{cite news|title=“Ring Ring!” — Heo Nam Jun dialling up new drama “When The Phone Rings” as a psychiatrist and content creator|url=https://theindependent.sg/ring-ring-heo-nam-jun-dialling-up-new-drama-when-the-phone-rings-as-a-psychiatrist-and-content-creator/|work=The Independent (Singapore)|date=21 October 2024}}</ref> The drama itself was a commercial success and received positive reviews.<ref>{{Cite web|title=Top 10 Non-English Most Watched TV-Shows (November 25 - December 01, 2024)|url=https://www.netflix.com/tudum/top10/tv-non-english?week=2024-12-01|website=Netflix|date=December 5, 2024}}</ref> Heo was also awarded the Best New Actor Award from the [[2024 MBC Drama Awards]] for his outstanding performance in the drama.<ref name="MBC Drama Awards">{{cite news|title="이가섭·허남준, 男신인상 공동 수상..첫 마디부터 "여객기 참사 희생자들께 애도를" ('MBC 연기대상')".|url=https://www.chosun.com/entertainments/broadcast/2025/01/05/YDTX6SGK5H6XYABDSHURUMFV7M/|language=Korean|work=Chosun Ilbo|date=5 January 2025}}</ref>
Heo was cast in [[TvN (South Korean TV channel)|TvN]] drama ''[[When the Stars Gossip]]'' (2025), which was first broadcasted on 4 January 2025.<ref name="스포츠동아">{{Cite web |date=20 December 2024 |title=이민호·공효진→오정세, 태양계 궤도 같은 인물관계도 (별들에게 물어봐)|url=https://sports.donga.com/ent/article/all/20241220/130688417/1 |website=스포츠동아 |language=Korean}}</ref><ref name="NE241120">{{Cite news|url=https://www.newsen.com/news_view.php?uid=202411200801266310|title=이민호 공효진 ‘별들에게 물어봐’ 드디어 본다‥내년 1월4일 편성 확정|publisher=Newsen|language=Korean|date=20 November 2024}}</ref>
