Like, there are leaves on the outside, and leaves on the inside which are usually protected from the elements.
I believe there aren't any words to describe this. Adhering to a phyllotaxy dictionary also doesn't yield good results.
You may want to use 'sheltered/shielded/inner foliage' or 'inter-verduary so-and-so' or even 'secluded leafage/foliage'.
Capitalizing on the 'covered' aspect, by using adjectives like 'umbriferous' (Meaning: casting shade or shadow), in a different syntax as opposed to your sentence can also, if done right, yield the same result.
I don't believe that there is a single term for this but I might be wrong.
I'd suggest something like 'delicate foliage', maybe with further circumscription.
The tree's inner delicate foliage, protected from harms of any sort by the shrouding outer leaves
"Shoot(s)", meaning emerging steam and embryonic leaves of a new plant, may be used.
A new growth on a plant whether from seeds or other parts is called 'SPROUT'It can be used as well.
At the simplest, "EAR" may have a chance