To help you as a new manager you get a bonus in your first seasons. This bonus takes up to 4 seasons. If you reset your account by leaving your club then you will again get the starters bonus after joining a new club.
When you have starters bonus you will have an increased popularity gain, increased income from your stadium and shorter building times.
The building time for all facilities is divided by 2. This is based on the moment when the construction was ordered. If you start construction on the last day of your starters bonus you still get the full bonus.
When you take over a fairly new advanced team it's possible that you can still get part of the beginners bonus. The beginners bonus is linked to the club, not to the manager. If the club has 2 seasons of bonus left when their manager leaves, the club still will get a bonus for 2 more seasons, even when a new manager would take over this club.
