여유 = 1) an extra amount of time, space, or money that gives you freedom, relief, or comfort. "breathing room". 2) composure. 여유가 있다 thus means being comfortable because one has enough of something, and 여유 있게 살다 would be living comfortably without financial worries. Since 얻다 means to gain or come into possession of something, 여유(를) 얻다 would mean to have breathing room (after being under pressure). We also say 여유가 생기다 or 여유를 찾다 for the same meaning. These expressions are rather vague though, because they are not saying what kind of relief or comfort. 시간 여유가 생겼다 (We now have some time to catch breath), 돈(을) 빌려 줄 여유가 없다 / 빌려 줄 여윳돈이 없다 (Too tight to lend someone any money / Have no extra money to loan someone), etc. are more specific examples.