I'm not sure what "In deep context" means here, but let me take on an answer for you, and if someone else wants to add something more, that will just enhance it :).
For an English speaker, think of this as two words. It's not in Korean, but as we think in English, we would have to express it as two words.
The first part is the 있다 which, of course, means exists, is present, is is there. This is the non-honorific form of this verb. Other forms of it are: 있습니다, 있습니까 (question form), 있어요, or the casual form of 있어. So, your boss looks into an office to see if your coworker is there. You might ask "있습니까?" ("Is he there?" Both the subject and PN are understood, so you don't need to pronounce them.). He may answer you "있습니다." or he may use one of the less formal versions of the word to answer.
하지만 means "But." You can take the 지만 and attach to another verb and it means " but," or "however." So in the case of your question, 있지만 would mean "it exists, but" or "it's there, but ... " and another clause with its own verb is expected to follow.
So going back to the example I used before, maybe your boss would answer "있지만 잡니다" to mean "He's there, but he's asleep. It might sound better to say "있지만 자고 있습니다" which would be more like "He's there, but he's sleeping."
I might have introduced something else that is confusing with conjunctions and present progressive with my last example, but hopefully not. If so, ask and we can clarify.