Yes, in pro sports the negotiation for a contract renewal often takes months if not years.
For players between contracts, the off-season will usually be several months, and many players won't sign until just before the season begins, negotiating with teams along the way.
Do you read the sports page? If you're the elite of the elite, yeah, hiring decisions are often quick. If you're only good enough to get drafted in the 3rd or later rounds, expect to spend a lot of time doing combines and visiting exercises and then be assigned to minor leagues. Even if you get called up, expect to be traded without your input unless you're the best of the best. Don't get injured. Even the best of the best can't always pick their teammates.
For players between contracts, the off-season will usually be several months, and many players won't sign until just before the season begins, negotiating with teams along the way.