(n.) the slow emergence of new leaves and buds; the time of year this occurs
The time of year when buds, flowers and new leaves begin to emerge—or the very process by which these new emergences take place—is called frondescence.
That’s a word dating back to the early 1800s in English, alongside it’s related adjective frondescent. In a more general sense, it’s also a word that can be used more loosely of the entire fully-formed foliage of a plant or tree.
At its root (no pun intended), frondescence derives from frons, the Latin word for a leaf. (Unsurprisingly, that’s also the origin of the fronds of a fern or palm.) From frons derived a verb frondere in Latin, which literally meant ‘to come to leaf’, or more loosely, ‘to turn green’—but from that in turn emerged a more specific verb form, which provides the etymological missing link here.
Frondere had a so-called inchoative verb form in Latin, frondescere, which meant specifically ‘to become green’, or ‘to begin to produce leaves’. Inchoative verbs are ultimately those that describe the beginning or becoming of a process; English uses the suffix –en to the same effect, to produce ‘becoming’ words like harden and soften, lighten and darken, whiten and blacken, and madden, sadden and gladden.
In Latin, the inchoative aspect of a verb was often driven by an infix, –sc–, which wheedled its way into the centre of the root word in question. So frondere, ‘to produce leaves’, became fronsescere, ‘to begin to produce leaves’. Likewise, Latin had verbs like frigescere (‘to grow cold’), algescere (‘to start to freeze’), horrescere (‘to become terrified’) and fatiscere (‘to grow week’). Just as in frondescence, some of these –sc– additions live on in English today, in words like adolescence (from Latin alescere, ‘to become nourished’), tumescence (from tumescere, ‘to begin to swell’), and evanescent (from vanescere, ‘to begin to vanish’). This element even provides the somewhat tricky spelling of the word convalesce, which comes from the Latin valescere, meaning ‘to begin to grow strong’.