간구(懇求)하다: to eagerly seek
This isn't a very common word but the two parts are:
- 간(懇) as in 간절(懇切)하다, which means "to be earnest". Commonly, you'll hear this as the adverb 간절히 (see VS + 게), which means "earnestly".
- 구(求) as in 구하다, which means "to seek".