Each answer is the title of a famous novel. A few of the titles are split into two clues - you should find those clearly marked.
Across
3 Think of the Phoenician, a possible drench, bleached prisons, or beach spindles (8,7)
Consider Phlebas ('Think of'=consider, Phlebas the Phoenician, three anagrams)
6 Three women (under training) - Russian tragedy (4,8)
Anna Karenina (Anna, Karen, Nina, under a train)
9 Before playing the numbers on an Air Serbia flight (9) (after 1 down)
Prejudice (Pre, airline code JU, Dice)
10 Fabric, for the (French) Nordic funeral (11,4) (after 23 across)
Huckleberry Finn (Huck, Le, "Bury Finn")
12 Liquid vessel sunk - in Hampshire? (9,4)
Watership Down
14 Ennobled for misplacing files (4,2,3,5)
Lord of the Flies
15 Impressive detective; an annoying producer of electronic music (4,4)
Moby Dick
17 A member of a Gallic mendicant religious order, spun unluckily - don't be silly (5) (before 4 down)
Sense (ROT13:FRAFR - abbrev:Friar, abbrev:France)
18 See a snotty cold; a dripping nose, it looks like. (1,4,4,1,4)
A Room With a View ("Rheum")
20 Terrifying German lunch assembled from parts: sausage'n'tankard (12)
Frankenstein (Frank 'n' Stein)
21 A number of Winston's wartime exploits (6,4) (second half, after 7 down)
Eightyfour
22 Agricultural earthquake in Filipino city (6,4)
Animal Farm (Anagram:MANILA, Farm)
23 After year zero, invests risk capital (10) (before 10 across)
Adventure (AD Venture)
Down
1 She's got a ticket to Ryde - starting at Portsmouth (5) (before 9 across)
Pride (P, "Ryde")
2 Anticipate the arrival of you, seen, with half a drum, floating downriver (3,10,2,3,6)
The Adventures of Tom Sawyer (Advent, "Saw yer", Tom-tom)
4 Sensitiveness, aesthetic appreciativeness, capacity of emotion (11) (after 17 across)
Sensibility
5 Initially rebellious sheep undertake a silent infantry operation, inside a small enclosure, or so I'm induced to believe (10)
Persuasion (initials "rsuasio" within "pen")
7 A number of Winston's wartime exploits (8) (first half, before 21 across)
Nineteen
8 Little-known Beatles song (without straw) (4,3,7)
Jude the Obscure ("Hey Jude" without "hay", little-known = obscure)
11 Computerised socialite gazes at beverage, a monarch writes (2)
It ('It' girl, information technology, eye tea, Stephen King)
13 Mr President, you sailed beyond the sunset to the sheltered end of the oceans, I've heard? (7)
Ulysses (You Lee Seas, quote from Tennyson's Ulysses, Ulysses S Grant)
16 Oscar eats a food rich in iron, then dances to Chubby Checker (6,5)
Oliver Twist (O, Liver, Twist)
19 Makin' twice as many female pronouns, in Ireland (9)
Dubliners ("Doubling Hers = Doublin' 'ers")
21 A tenth of a centimetre of MDMA for the electric André-Marie - clueless? (4)
Emma (E, mm, Ampere, 'Clueless' movie has plot of Emma)
Do ask if you have any questions, either in the comments or ping me on chat with an '@AE'.
In the spirit of teamwork, partial answers are very welcome.
Answers providing constructive feedback on the puzzle itself - how hard it is, what could be improved - are also very welcome. This puzzle took me ages to compose, so please be kind! ;)
Update:
All answers now added. Thanks to all the solvers! :)