Church clocks appear as soon as clocks appear - by which I mean, the earliest church clocks in Europe can be dated to around the same time that mechanical clocks develop in general, c.1280-1320AD.

The 'mechanical clock' differs from earlier clocks, where the escapement (the rotating cog) was powered by a hydraulic system, which required frequent resetting and rotating. Mechanical clocks were instead powered by gravity, using a weight to transfer energy to the escapement, which in turn powered a balance bar called a foliot which regulated the movement. This meant that they were substantially easier to maintain, requiring less frequent intervention - and, as such, were suitable for installing at height, on the exterior wall or tower of a church, cathedral, or monastery.

The very earliest church clock is uncertain, although it has been proposed that the clock in Dunstable Priory might have been the first, built in 1283. There are surviving examples in the West of England (Salisbury Cathedral, Wells Cathedral), at Beauvais in France, and in the Venetian lagoon, all of which date to the late 13th or early 14th centuries. Many 14th and 15th century verge clocks were converted to pendulum clocks when that technology developed in the 17th century, because it was more accurate.

If you think about it, it makes sense that religious buildings would house clocks, as soon as clocks became mechanically and structurally viable. Clocks were manifestations of science and scholarship, and scholarship in the medieval period was very much in the hands of the church - even the great universities, like Oxford, Paris and Bologna were ecclesiastical establishments. On a more mundane level, the parish church - or, in an urban setting, the cathedral - was the most significant building in most people's immediate locale. The church was not just a place of spiritual significance, but a place of social interaction, where the most important events of a life - baptism, marriage, funeral - would be staged. So it makes sense that the church marked time, literally. They were public spaces, and authoritative spaces - and only the very, very wealthiest private individuals would have owned a clock in this period.