Lord Brahma has a lifespan of 100 Brahma years (one day of Brahma is 1000×1 MahaYuga) and after that he dies.
What is time interval between the death of the old Brahma and the birth of a new Brahma?
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One hundred years of Brahma. The period between the death of the old Brahma and the birth of a new Brahma is known as a Mahapralaya or Prakritika Pralaya, and it's described in this chapter of the Vishnu Purana:
I will now, Maitreya, describe to you elemental dissolution. When by dearth and fire all the worlds and Pátálas are withered up, and the modifications of Mahat and other products of nature are by the will of Krishńa destroyed, the progress of elemental dissolution is begun. Then, first, the waters swallow up the property of earth, which is the rudiment of smell; and earth, deprived of its property, proceeds to destruction. Devoid of the rudiment of odour, the earth becomes one with water. The waters then being much augmented, roaring, and rushing along, fill up all space, whether agitated or still. When the universe is thus pervaded by the waves of the watery element, its rudimental flavour is licked up by the element of fire, and, in consequence of the destruction of their rudiments, the waters themselves are destroyed. Deprived of the essential rudiment of flavour, they become one with fire, and the universe is therefore entirely filled with flame, which drinks up the water on every side, and gradually overspreads the whole of the world. While space is enveloped in flame, above, below, and all around, the element of wind seizes upon the rudimental property, or form, which is the cause of light; and that being withdrawn, all becomes of the nature of air. The rudiment of form being destroyed, and fire deprived of its rudiment, air extinguishes fire, and spreads resistlessly over space, which is deprived of light when fire merges into air. Air then, accompanied by sound, which is the source of ether, extends every where throughout the ten regions of space, until ether seizes upon contact, its rudimental property; by the loss of which, air is destroyed, and ether remains unmodified: devoid of form, flavour, touch, and smell, it exists unembodied and vast, and pervades the whole of space. Ether, whose characteristic property and rudiment is sound, exists alone, occupying all the vacuity of space. But then the radical element egotism devours sound, and all the elements and faculties are at once merged into their original. This primary element is consciousness, combined with the property of darkness, and is itself swallowed up by Mahat, whose characteristic property is intelligence; and earth and Mahat are the inner and outer boundaries of the universe. In this manner, as in the creation were the seven forms of nature (Prakriti), reckoned from Mahat to earth, so, at the time of elemental dissolution, these seven successively reenter into each other. The egg of Brahmá is dissolved in the waters that surround it, with its seven zones, seven oceans, seven regions, and their mountains. The investure of water is drunk up by fire: the stratum of fire is absorbed by that of air: air blends itself with ether: the primary element of egotism devours the ether, and is itself taken up by intellect, which, along with all these, is seized upon by nature (Prakriti). Equilibrium of the three properties, without excess or deficiency, is called nature (Prakriti), origin (Hetu), the chief principle (Pradhańa), cause (Kárańa), supreme (Param). This Prakriti is essentially the same, whether discrete or indiscrete; only that which is discrete is finally lost or absorbed in the indiscrete. Spirit also, which is one, pure, imperishable, eternal, all-pervading, is a portion of that supreme spirit which is all things. That spirit which is other than (embodied) spirit, in which there are no attributes of name, species, or the like--which is one with all wisdom, and is to be understood as sole existence--that is Brahma, infinite glory, supreme spirit, supreme power, Vishńu, all that is; from whence the perfect sage returns no more. Nature (Prakriti), which I have described to you as being essentially both discrete and indiscrete, and spirit (which is united with body), both resolve into supreme spirit. Supreme spirit is the upholder of all things, and the ruler of all things, and is glorified in the Vedas and in the Vedanta by the name of Vishńu.... The period of two Parárddhas, as I have described it to you, Maitreya, is called a day of that potent Vishńu; and whilst the products of nature are merged into their source, nature into spirit, and that into the supreme, that period is termed his night, and is of equal duration with his day. But, in fact, to that eternal supreme spirit there is neither day nor night, and these distinctions are only figuratively applied to the almighty.
So as you can see, the duration of a Mahapralaya is equal to two Parardhas or one Mahakalpa. That is one hundred years in the life of Brahma, as described in another chapter of the Vishnu Purana:
The Krita, Tretá, Dwápara, and Kali, constitute a great age, or aggregate of four ages: a thousand such aggregates are a day of Brahmá, and fourteen Menus reign within that term.... Of such days and nights is a year of Brahmá composed; and a hundred such years constitute his whole life. One Parárddha or half his existence, has expired[.]