English Translation
I don’t know if I have the time.
있는지: whether there is, present tense of 있다 (to exist/be present)
More examples of using 지 in this way:
먹은지 오래됐어요. (It's been a long time since I ate.)
알아보는지 좀 더 시간이 필요해요. (I need more time to investigate whether it's true or not.)
살아있는지 확인해 보세요. (Please check whether it's alive or not.)
만나본지 언제인가요? (When was the last time you met?)
차가운지 느껴지지 않아요? (Don't you feel it's cold?)
알고 있는지 물어보세요. (Ask whether they know or not.)