To find an absolute answer, we will need to know what kind of clock are you talking about. People in ancient times used to use sundials, devices with certain angles and measurements which would determine time on the direction and size of the shadow of a central needle.
Then come the water clocks, which have been found to have existed since 16 century BC, with no clear idea on any person who might have invented them.
The most recent form of a clock, prior to the digital age, we find as geared clocks which we also call by the name of analog clocks. The first geared clock, which was a water mechanical clock, was invented by Archimedes somewhere around the 3rd century BC. Later, Andalusian scientist Ibn Khalaf Muradi did great work to improve it. And those inventions through many and many ages of evolution are seen today as we see them hanging on our walls.