According the the Tintern Abbey guidebook, Tintern Abbey was founded by Walter fitz Richard of Clare (d. 1137) the Anglo-Norman lord of Chepstow, in 1131. It was the first Cistercian Abbey in Wales.
Over the previous half-century the Normans had introduced Benedictine priories, founded as dependencies of large Abbey’s in England or France, as a way to use religion to control the populace of Wales. It is not an uncommon move for unpopular conquerors. The Welsh Church had a strong independent streak (not unlike its people), and that was certainly part of the motivation too.
Over the centuries, the Lords of Chepstow (including William Marshal and Roger Bigod) continued to support Tintern. Although Cistercians eschewed inhabited or manoral lands as gifts, they were given them anyway, and thus the lands controlled by Tintern expanded over the years.
By a 1291 tax survey, the monks at Tintern were farming over 3000 acres on the Welsh side of the Wye and had 3264 sheep. They were assessed taxes of 145 pounds.