You need to place your clip on the timeline, select it, then click the “filter” tab, then press the “+” icon , then you can search for the filter by typing “noise…”
However, this Noise gate filter was only introduced in version 19.12 (December 2019), which is easily downloadable from here: https://shotcut.org/blog/new-release-191216/
As an alternative, you could
Import your footage into Shotcut. Detach the audio so it appears on an audio track.
2 Export as an mp3. Close Shotcut.
Open the mp3 in Audacity.
Apply Noise reduction in Audacity. Export. Give it a new name.
Re-import the new audio file into SC to replace the original.