This is also an old Celtic tradition, originating in pagan ritual but which has become a common feature of Irish Catholic pilgrimage traditions.
At the Shrine of Our Lady of Knock, people circumambulate the church anti clockwise.
At the stations of St. Patrick on Croagh Patrick, people circumambulate anti-clockwise.
At Saint Patrick’s Purgatory, people circumambulate clockwise.
At Teampall Colmcille in Gartan, the birthplace of St. Columba, people circumambulate anti clockwise.
Conclusion: Depends on the tradition of the particular shrine or church. If in doubt, just go whatever way you think is best.
Final piece of advice, remember that there is no power in the act of circumambulation, it has no value in itself, it serves merely as a reminder of our need to place the faith at the centre of all our actions, that our actions must “orbit” the faith so to speak.