다가서다 (tagaseoda) means “approach”

More examples

고양이가 내 옆에 바짝 다가섰다.ko yang i ga nae yeo pe pa jjak ta ga seot tta

The cat came right up beside me.

Moving toward a person or place until standing close to it.

다가가다tagagada: Go toward a person or place until reaching a nearby position.
다가오다tagaoda: Come nearer to the speaker or another reference point.
가까워지다kakkawojida: Become nearer than before in physical distance or time.

어떤 대상에 몸을 옮겨 가까운 위치에 머무르다.eo tteon tae sang e mo meul om gyeo ka kka un wi chi e meo mu reu da

다가 (daga, "nearer") and 서다 (seoda, "to stand") join to express coming near and remaining in that position.

The verb is useful for scenes in which someone closes the distance before an interaction, not just for motion from one place to another.