/n/ → /ŋ/
Here the /n/ is followed by a sound that is produced at the back of the mouth, a velar (a /k/or a /g/), so the nasal alveolar /n/ is turned into a nasal velar /ŋ/. As you can see, the place of articulation changes, but the manner is the same.
Therefore,
/n/ (followed by /k/ or /g/) becomes /ŋ/
One king. ǀ wʌŋ ˈkɪŋ ǀ
Then go for it! ǀ ˈðeŋ ˈgəʊ fər ɪt ǀ
This is the type of work I do with my students in my one-to-one classes. I make them practise these processes with exercises until they improve their comprehension of native speakers and are capable of speaking like that themselves. If you are interested in my classes, you can contact me here.