I'd like to know an adjective to describe age between young and old. I know middle age is such a word, but it is a noun phrase. Is there an adjective for it?
Middle-aged functions as an adjective.
You could also call the individual by the name of his/her generation (millennial, baby boomer, etc.). There are also technical names for people in their twenties, thirties, and so on. But these names are uncommon.
You could also communicate the age of the individual by describing him/her with the key characteristics of most middle-aged people: gray-speckled, beer-bellied, double-chinned, stubble-ridden, white-sneakered, etc.
I'd suggest "prime age", and here prime is an adjective.
Young age has no precise perception. It could be the infant stage, or one's adolescence. So it is a wide range of ages, unlike old age which is a considerably lesser range. Prime age is the age where one is usually at the peaks of their career. It also can be seen as a wide range, but definitely prime age is when one is older than what would be considered young. It could be from 25 years to 50.