The 'Puritan Period' belongs to-

Puritanism, a religious reform movement in the late 16th and 17th centuries that sought to “purify” the Church of England of remnants of the Roman Catholic “popery” that the Puritans claimed had been retained after the religious settlement reached early in the reign of Queen Elizabeth I.
Puritans became noted in the 17th century for a spirit of moral and religious earnestness that informed their whole way of life, and they sought through church reform to make their lifestyle the pattern for the whole nation. Their efforts to transform the nation contributed both to civil war in England and to the founding of colonies in America as working models of the Puritan way of life.

King Henry VIII separated the Church of England from the Roman Catholic Church in 1534, and the cause of Protestantism advanced rapidly under Edward VI (reigned 1547–53).

SO, concluding this discussion,
'The Puritan Age' reders the time from 1530s to 1660.
And, The Renaissance Period (1500-1660) of English Literature had also happend that time.
It is divided into four shorter period.
These are:
1. Elizabethan Period (1558-1603),
2. Jacobean Period (1603-1625),
3. Caroline Period (1625-1649) and
4. Commonwealth Period (1649-1660).
So, All these periods also belong to the Puritan Period.

Source: Britannica.com and History.com