Is there a word that means “measure time”?
If you're measuring the time it takes a runner to run 100 meters, you are timing the runner, or clocking the runner.
From Merriam-Webster dictionary:
Clock: transitive verb 1a: to time with a stopwatch or by an electric timing device
Time: transitive verb 4. to determine or record the time, duration, or rate of
To time conveys the meaning you want:
If you time an action or activity, you measure how long someone takes to do it or how long it lasts.
- He timed each performance with a stop-watch.
(Collins Dictionary)