たて, coming from the verb 立（た）てる ‘to stand’ is a 接尾語（せつびご） (suffix) in Japanese that is often used after the 連用形（れんようけい） (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 格助詞（かくじょし） (case marking particle) の and a noun.
Everything here is freshly fried.
It is just fished up, so it is fresh!
I like to eat freshly baked bread.
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.
Making salad with freshly picked vegetables is delicious.
These shoes got freshly wet, so it will take some time to dry.