Do children need to apply for TSA PreCheck®?

It depends on their age and whether they are traveling with a parent or guardian who has enrolled in TSA PreCheck:

Please note, adults using gate passes to accompany children traveling alone will be directed to standard screening as gate passes are excluded from TSA PreCheck benefits. This applies even if the gate pass holder has enrolled in TSA PreCheck. The adult will not be permitted to join the child in the TSA PreCheck lane.

Please note, no individual is guaranteed expedited screening because TSA uses unpredictable security measures, both seen and unseen, throughout the airport. All travelers will be screened, and no individual is guaranteed expedited screening.