たて, coming from the verb 立（た）てる 'to stand' is a
suffix in Japanese that is often used after the
conjunctive form of verbs. たて conveys that something has 'just been finished', or is 'freshly finished'.
As a
suffix, たて transforms verbs into nouns. This means that they may be followed by a (B) phrase, or followed directly by the
case marking particle の and a noun.
ここにあるのは全部（ぜんぶ）揚（あ）げたてですよ。
Everything here is freshly fried.
釣（つ）りたてだから新鮮（しんせん）だよ！
It is just fished up, so it is fresh!
私（わたし）は出来（でき）立（た）てのパンを食（た）べるのが大好（だいす）きです。
I like to eat freshly baked bread.
生（う）まれたての赤（あか）ちゃんっておさるさんみたいじゃない？
Don't newborn babies look like monkeys?
たて is a
suffix that is used to convey the moment in time directly after something has been finished, rather than the fact that it 'is' finished. Due to this, たて is most frequently used with verbs that indicate some sense of time based importance, where (A) will degrade in quality over time after completion.
取（と）り立（た）ての野菜（やさい）で作（つく）るサラダは美味（おい）しい。
Making salad with freshly picked vegetables is delicious.
この靴（くつ）は濡（ぬ）れたてだから、乾（かわ）かすのに少（すこ）し時間（じかん）がかかると思（おも）う。
These shoes got freshly wet, so it will take some time to dry.