〜たて
freshly (done), just (made)
Verb ます-stem + たて (の + Noun)
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たて after a ます-stem means something has only just been done, and is still fresh: 焼きたてのパン, "freshly baked bread"; できたての料理, "freshly made food".
It works like a noun and takes の before another noun. It's common with food (焼きたて, 揚げたて, 取れたて) and for things that are brand new (塗りたてのペンキ, "wet paint"; 大学を出たての新人, "a new graduate").
Compare たばかり (N4), which is "just did" for any action and works as a verb phrase. たて is more limited and describes a fresh state, usually positive.
You'll see it on shop signs and menus all the time.
Examples
焼きたてのパンはおいしい。
Freshly baked bread is delicious.
できたての料理をどうぞ。
Please enjoy the food while it's fresh.
塗りたてのペンキに注意。
Caution: wet paint.
彼は大学を出たての新人だ。
He's a new recruit, fresh out of university.
取れたての野菜を売っています。
We sell freshly picked vegetables.