Many think that reciting the Qur’an is just during the day when fasting whereas the Prophet (saw) would meet Jibreel (as) in the night. So, try to read some Qur’an at night too.
Also, remember that if you can, even if it’s only 5 minutes, pray more after tarawih. A person may pray tarawih, go home and miss out on the blessed last third of the night.
Finally, do some istighfar in the time just before fajr as this was the practice of the Sahaabah and the righteous of the past.