Last 4 - stuck in the bottom right corner
The first three contain a letter in the clue that needs to be disregarded to parse the answer.
13d Historic document promoted cause of abstract artist to preserve school. (5,5)
_ A _ N _ / _ _ R _ A
This looks like Magna Carta. but if it is I can't parse it! (By the way the letter to be disregarded in the clue is a "U"
19d Unmarried woman that raised triplets maddens nurses (6) _ _ _ S _ L
(the letter to be disregarded is a "T")
20d Neighbour lied to judge in a murder case (6) _ _ _ O _ N
(the letter to be disregarded is an "E")
This next one is a themed answer which is not defined, therefore the clue is just the parsing without the definition. Without giving the theme away it needs to be someone's surname)
23a Host passing fancy retreat (8) _ _ _ _ _ _ _ N
the 6th letter of 13d is the second letter of this one (C if magna carta)
the second letter of 19d is the 4th letter here
the second letter of 20d is the 6th letter here
If it is Magna Carta the only themed answer I can come up with is SCHEKMAN but this doesn't parse and so I am not sure that Magna carta is correct