With regard to the lesson which some imams and preachers give after four rak'ahs of Taraaweeh, there is nothing wrong with it in sha Allaah, but it is better not to do that all the time lest the people think that it is part of the prayer and lest they think it is obligatory and denounce the one who does not do it.
The imam, teacher or preacher can draw the people’s attention to a few shar’i rulings, especially those that they need to know in this month of matters, provided that he does not do that every time.
Undoubtedly words such as these are more beneficial than going out or engaging in worldly conversations or raising one’s voice, and it is better than innovated dhikrs that some imams have introduced after completing four rak’ahs.
Shaykh ‘Abd-Allaah ibn Jibreen said:
Because people nowadays make the prayers short and do it in an hour or less, there is no need for them to have this rest, because they do not get tired or find it difficult. But if some imams separate the rak’ahs of Taraaweeh by sitting or by pausing to catch their breath, then it is better to use this rest to offer some advice or give a reminder, or to read from a useful book, or to give some tafseer (commentary) on a verse that the imam has recited, or to give a lesson or reminder of an Islamic ruling, so that the people will not leave or get bored. And Allaah knows best.
Al-Ijaabat al-Bahiyyah fi’l-Masaa’il al-Ramadaaniyyah (Question 2)
And Allaah knows best.