So you are at High Gate ruins?
Take a follower with you, climb up the hill of rubble in the room past where Anska is and get on the walkway above, your follower not being able to get up there that way, will run around and go through the locked door to meet you. Get them to open the door for you, there is a chain on the other side for them to pull. You might need to ask them to do something before getting up there, but I do not remember having to. I was after a book for Urag.
You would think after all this time Bethesda would have got the doors to stay open.