In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Muslims should perform Tarawih prayer after Isha on the first night of Ramadan, which is the night on which the new moon is sighted or Muslims complete thirty days of Shaban.
In responding to your question, the Fatwa Center at Islam Q and A, states:
Similarly at the end of Ramadan, Tarawih prayer should not be offered if it is proven that the month has ended, either by sighting of the new moon of Eid or if the month of thirty days has been completed.
It is clear that Tarawih prayer is not connected to the fast during the day in Ramadan, rather it is connected to the onset of the month at night in the beginning, and the last day of Ramadan at the end.
We should not say that Tarawih prayer is a nafl prayer and it is permissible to offer it on any night and in congregation, because tarawih prayer is limited to the month of Ramadan, and those who offer this prayer are seeking the reward that comes for praying it.
The ruling on offering this prayer in congregation is different from the ruling on offering other prayers in congregation. In Ramadan, it is permissible to pray tarawih in congregation on each night, whilst announcing it and encouraging others to join, unlike qiyam at other times, where praying qiyam in congregation is not part of the Sunnah unless it is done without having the intention beforehand, or it is done for the purpose of encouraging and teaching others. So it is Sunnah to do it sometimes without committing to doing it all the time or persisting in that.
Sheikh Muhammad al-Salih al-Uthaymeen (may Allah have mercy on him) said:
Tarawih at times other than Ramadan is an innovation (bidah). For example, if the people wanted to gather to pray qiyam in congregation in the mosque at times other than Ramadan, this would be an innovation.
There is nothing wrong with a person praying in congregation in his house occasionally at times other than Ramadan, because this is what the Prophet (peace and blessings of Allah be upon him) did. Once he led Ibn Abbas, and once Ibn Masud and once Hudhayfah ibn al-Yaman, in prayer in his house, but he did not adopt that as a regular Sunnah and he did not do that in the mosque.” (Al-Sharh al-Mumti’, 4/60-61)
Based on this, whoever offers Tarawih prayers before it is proven that Ramadan has begun is like one who offers a prayer at the wrong time. No reward will be written for him, even if he is free of the sin of doing that deliberately.
Almighty Allah knows best.