간구하다

From Jonathan Gardner's Korean Notebook

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".