The films make it seem like little time passed, but in the books it was years and years. Gandalf was trying to discover the true nature of the ring, so the only lead he had at the time was Gollum. He enlisted Aragorn to help, and they spent around 15 years searching together with no luck. Gandalf eventually gave up, which led him to Minas Tirith (as seen in the movie when he finds Isildur’s account of the ring). Aragorn kept searching, and he eventually caught Gollum in the Dead Marshes. After that, he took a long road to bring Gollum to the elves in Mirkwood, where Gandalf arrived to interrogate. This is how Gandalf knew so much about Gollum’s backstory. After getting the info he needed, it was agreed that Thranduil would keep Gollum locked up, but in a shock to no one, Gollum escaped (just like the dwarves in the Hobbit). Thranduil really needs to check the security of his cells. When you live forever, two escapes over a 100 year period is pretty bad