The phrase "ancient festival" is correct and usable in written English.
You can use it when referring to a festival that has historical significance or has been celebrated for a long time.
Example: "The ancient festival of Diwali is celebrated by millions around the world, marking the victory of light over darkness."
Alternatives: "historic celebration" or "time-honored festival".
Easter is an ancient festival of rebirth, but it's also an excellent excuse for eating eggs.
Wyre 27 28 July Cherry Festival (Bewdley Museum): traditional summer celebration of an ancient festival, with music, activities and stalls.
Thesmophoria, in Greek religion, ancient festival held in honour of Demeter Thesmophoros and celebrated by women in many parts of the Greek world.
It also posted it on the White House Web site, to coincide with Iranian observance of the ancient festival of Nowruz, which celebrates the arrival of spring.
I have always trusted that out of opera, as out of the choruses of the ancient festival of Bacchus, tragedy would liberate itself and develop in a nobler form.
In a clearing nearby, an oak branch had been stripped and erected as a maypole, and a firepit dug for the night's ceremony: the ancient festival of Beltane, or Walpurgisnacht.
Some countries have continued to observe ancient festivals; for example, Durga-puja, honouring the goddess Durga, remains an important festival in India.
At this year's Olympics in Athens visitors will find at their disposal hotels, restaurants and transportation of many types, but at the ancient festivals there was nothing of the kind.
The duties assigned to them at very ancient festivals, such as the Lupercalia (a fertility festival) on February 15, and at other occasions indicate their unique position and significance in the state cult going back, in all probability, to their origins in the family tradition, associated with the pontifices as the officiating priests.
The egg is as central to the commemoration of Easter as it once was to the ancient festivals in honor of the fertility goddess Eostre.
That is, May Day as in the ancient pagan festival, not the workers' holiday.
