Yeah they have life cycles.

The stage at the beginning, or rebirth, of a forest is known as an early successional stage. Essentially the area starts with plants such as moss, shrubs etc. This land over time transitions into a forest (depending on its location). Natural disturbances can destroy forests but over time it will go through the stages and eventually rebound.

There is debate on whether forests have a “climax stage.” In other words, a stage at which the forest reaches where changes no longer occur. I do not know too much about that debate so I’ll link an article when I find it.