Assalaamu alaykum wa rahmatullaahi wa barakaatuhu. I was not focused and did not realise what I was doing and broke the edge of a date palm tree's leaf by the roadside. If there any sin on me? What am I to do now?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

You bear no sin for what you did while you were not focused. It is a pardoned mistake. The Prophet, sallallahu ‘alayhi wa sallam, said, “Allah has forgiven my nation their mistakes and forgetfulness and what they are forced to do.” [Ibn Maajah and Al-Bayhaqi]

However, the fact that you bear no sin for it does not mean that you are not liable for compensation if this palm tree is someone's property.

The Kuwaiti Encyclopedia of Fiqh reads, “Scholars of Fiqh agreed that the compensation is due for any loss incurred on someone's wealth on account of unlawful usurping, harmful action, damage, or the like whether it is done deliberately or out of mistake or neglect.”

Hence, if the palm tree is owned by a person or an entity and the damaged part is significant and not normally excused, you are liable for compensating the owner with its value, but if the damaged part is insignificant and is normally excused, you are not liable for anything.

Allah knows best.