When God created Adam and Eve, He placed them in a garden that provided everything they needed to live. He told them, “Every plant yielding seed that is on the surface of all the earth, and every tree which has fruit yielding seed, it shall be food for you”. Genesis 1:29. (See also Genesis 2:9.)

Thus, while living in the garden, Adam and Eve ate a plant-based diet.  Later, after the flood, we are told that God included animals as man’s food. “And God blessed Noah and his sons, and said to them, ‘be fruitful and multiply, and fill the earth. The fear of you and the terror of you will be on every beast of the earth and on every bird of the sky; with everything that creeps on the ground, and all the fish of the sea, into your hand they are given. Every moving thing that is alive shall be food for you; I give all to you, as I gave the green plant.’” Genesis 9:1-3

Since God gave Adam and Eve plants to eat when He created them, surely there will be plants to eat in the kingdom.  

As to whether or not man will also eat animals, we cannot say for certain. Some scriptures seem to suggest not. Isaiah 11:6-9 says, “and the wolf will dwell with the lamb, and the leopard will lie down with the young goat, and the calf and the young lion and the fatling together; and a little boy will lead them.  Also, the cow and the bear will graze, their young will lie down together, and the lion will eat straw like the ox. The nursing child will play by the hole of the cobra, and the weaned child will put his hand on the viper's den. They will not hurt or destroy in all My holy mountain (kingdom) for the earth will be full of the knowledge of the Lord as the waters cover the sea.” 

So in the kingdom, animals who once ate other animals will no longer do so

One essential food that will sustain everlasting human life will be fruit from the Tree of Life. After Adam sinned, God specifically barred him from eating that fruit – “lest he reach out his hand and take also of the tree of life and eat, and live forever—” Genesis 3:22. 

But in Christ’s kingdom, all who desire may eat from the tree of life and drink the water of life. Revelation 22:1-2 (NIV), “…the river of the water of life… flowing from the throne of God and of the Lamb…On each side of the river stood the tree of life, bearing twelve crops of fruit…And the leaves of the tree are for the healing of the nations.”