pace¹ / pās/ • n. 1. a single step taken when walking or running. ∎  a unit of length representing the distance between two successive steps in walking. ∎  a gait of a horse or other animal, esp. one of the recognized trained gaits of a horse. ∎ poetic/lit. a person's manner of walking or running: I steal with quiet pace. 2. consistent and continuous speed in walking, running, or moving: most traffic moved at the pace of the riverboat | [in sing.] walking at a comfortably fast pace. ∎  the speed or rate at which something happens, changes, or develops: the children work separately in the classroom at their own pace the poor neighborhoods fester at an increasingly rapid pace. ∎  (in sports) the speed or force of a hit or pitched ball.• v. [intr.] walk at a steady and consistent speed, esp. back and forth and as an expression of one's anxiety or annoyance: we paced up and down in exasperation | [tr.] she had been pacing the room. ∎  [tr.] measure (a distance) by walking it and counting the number of steps taken: I paced out the dimensions of my new home. ∎  [tr.] lead (another runner in a race) in order to establish a competitive speed: Morales paced us for four miles. ∎  (pace oneself) do something at a slow and steady rate or speed in order to avoid overexerting oneself: Frank was pacing himself for the long night and day ahead. ∎  [tr.] move or develop (something) at a particular rate or speed: the action is paced to the beat of a perky march | [as adj. in comb.] (-paced) our fast-paced daily lives. ∎  [intr.] (of a horse) move in a distinctive lateral gait in which both legs on the same side are lifted together, seen mostly in specially bred or trained horses.PHRASES: change of pace a change from what one is used to: the magenta is a change of pace from traditional red.keep pace with move, develop, or progress at the same speed as: fees have had to be raised a little to keep pace with inflation.off the pace behind the leader or leading group in a race or contest.put someone (or something) through their (or its) paces make someone (or something) demonstrate their (or its) qualities or abilities: the cars are examined by our safety experts and put through their paces by our drivers.set the pace be the fastest runner in the early part of a race. ∎  lead the way in doing or achieving something: space movies have set the pace for the development of special effects.pace² / ˈpāˌsē; ˈpäˌchā/ • prep. with due respect to (someone or their opinion), used to express polite disagreement or contradiction: narrative history, pace some theorists, is by no means dead.

pace.
1. Part of a floor raised above the general level; a daïs.

2. Broad raised step around a tomb-structure, altar, etc.

3. Landing in a stair, especially the area where the stair turns. A half-pace is a landing where one flight ends and another begins, involving a turn of 180°. A quarter-pace is a landing between two flights involving a turn of 90°.

pace1 step; rate of progression; †step of a stair, floor raised by a step; †mountain pass. XIII. ME. pa(a)s — (O)F. pas — L. passus step, pace, lit. ‘stretch (of the leg)’, f. pass-, pp. stem of pandere stretch, extend.
Hence pace vb. walk with measured pace (along) XVI; set the pace for XIX.

pace it is the pace that kills proverbial saying, mid 19th century, used as a warning against working under extreme pressure.
put someone through their paces make someone demonstrate their abilities.
set the pace lead the way in doing something (literally, be the fastest runner in the early part of a race).

pace2 by leave OF. XIX. — L., abl. of pāx PEACE, as in pāce tuā by your leave.