very strict in moral or religious matters, often excessively so; rigidly austere.

( sometimes initial capital letter ) of, pertaining to, or characteristic of Puritans or Puritanism.

adjective

abstinent , austere , conforming , moral , priggish , prim , prissy , prudish , rigid , stern , strict , stuffy , bluenosed , old-maidish , precise , proper , strait-laced , victorian , genteel , straitlaced