I have seen a plethora of examples of sentences which use the word 'trot' in the context of horse gait, meaning a moderately paced running of the horse which is faster than horse's walking but slower than galloping. What I want to know is that if the word could be used for humans as well, in the sense that it would mean faster than leisure walking but slower than running?
Yes -- in fact nearly any animal characteristic can be (and likely has been) applied figuratively to humans. "Trot" would, as you say, be interpreted as movement faster than a walk but slower than a run, akin to jog.
"Lunch time!" the matron called. The boys obediently trotted from the playing field into the dining hall, where they lined up behind their assigned seats.
In the same way you could use "gallop" to indicate a fast run. "Canter" is possible, but doesn't work as well for humans, since it's an intermediate gait that only makes sense if you have four legs.
Other verbs commonly used for animal locomotion may be applied to humans, such as lope, fly, soar, prance, flutter, flit, hover, buzz and various others.