Luke 13.

3/5 "I tell you, no! But unless you repent, you too will all perish."

9"If it bears fruit next year, fine! If not, then cut it down.' "

( Even if for this parable is no immediate explanation of Jesus we can assume that the tree represents a person who belongs to this owner of the vineyard. This owner should be God than. The man who takes care of this tree might be Jesus but it can also be workers of God... brothers and sisters in the church who intercede for one another)

A task for everyone to complete in order to avoid from perishing but us is given patience for it.
In German these two things are separated but in the English version they are in one section. I think that they do relate to each other. Jesus said the nice story with the tree maybe to comfort them and say that even fruits are demanded that God will not be unfair or very strict. He will give us time to do it and when he looks for the fruit he search for it every year. But when we are too weak to bear a fruit than we will receive support from outside through fertilizers for better nutrients and a loosened soil for a better development of the roots.
This story tells beside the patience, love and care of God also his righteousness.
The reason why this tree should be cut is because it uses up the soil without bearing a fruit.
It is probably not worthy to receive the nutrients from the soil and which other plants might need. So an improvement is demanded.
So if this tree does not change, repent and bear fruit it will perish.