여유 부릴 때 is composed as 여유 부리(다) + ㄹ/을 때 여유 means " room; space; spare time; composure" 여유(를) 부리다 means "to relax; to be relaxing" ㄹ/을 때 means "time to do something" or "when doing something" 때 can be used as the noun being described in the ~는 것 principle. When used like this, it indicates a specific moment in which something happens. The future tense form of ~는 (~ㄹ/을) is usually used to describe 때 in these cases. For example: 내가 밥을 먹을 때 This construction translates to something like “the time that I eat.” 지금은 여유 부릴 때가 아니다 It's not the right time to be relaxing. 그렇게 여유부릴 때가 아닐텐데 means I guess that it's not the time for you to be such relaxing.

여부리다 just means 'to relax' So if someone says "그렇게 여유부릴 때가 아닐텐데" it would mean something like, "This isn't the time to relax"