In parathyroid hyperplasia, there is little or no adipose tissue, but any or all cell types normally found in parathyroid are present. Note the pink oxyphil cells here. This is actually "secondary hyperparathyroidism" with enlarged glands as a consequence of chronic renal failure with impaired phosphate excretion. The increased serum phosphate tends to drive serum calcium down, which in turn drives the parathyroids to secrete more parathormone.