Bridle
A bridle was a harness for horseback riding. 

One component of the bridle was the bit, which was placed in their mouth and used by the rider to communicate with the animal, to "champ" or "chomp on the bit" was an Earth idiom used to mean to be impatient or frustrated with a delay. 

When Captain Jonathan Archer denied 's request to join the boarding party of a derelict Axanar cargo ship in 2151, Tucker complained to the captain, that "[y]ou're chomping at the bit to find out what's in there. Why should I be any different?" ()

The following year Archer explained to T'Pol that Doctor Phlox had already left for the IME Conference, as "[h]e was champing at the bit to get down to that conference." ()

When  was investigating a hypergiant star in 2153, Archer gave Astrometrics the go ahead to begin their scans, adding, "I'm sure they're champing at the bit." ()

In 2254, illusory versions of two horses owned by Christopher Pike – Tango and Mary Lou – each wore a bridle. The bridles and everything else in the illusion were telepathically created by the Talosians. ()

Jean-Luc Picard's holographic horse from the Equestrian Adventure holoprogram also wore a bridle. ()

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