A good puzzle with a variety of devices. I found it tough and perhaps not as straightforward as the author claims. It took me two sessions to solve the puzzle.
There are several occasions where words have to be separated and where hyphenated words are treated as if the hyphen weren't there. There's also more repositioning, i.e. changing the order of wordplay parts, than usual. That's by no means unfair, though, and once you start looking for these devices, the puzzle yields steadily.
(Below, definitions are in hold. Not all positional indicators are explained, but should be clear.)
Completed Grid
B A C T R I A N C A M E L
L A U S O A O
B U R N B A S I C B I T C H
S O E O O L K
O H W E L L C R O W F O O T
E L I N R U
B R E A K A W A Y L A S T
R T U
A I R S B E H E A D I N G
T O D D X A
S H O W C A S E P R I O N S
E H C G O S K
F I R E S T O R M S I D E A
S A Y E E T E
M I D D L E E A S T E R N
Across
1 Changing climate? Ban car transport (8,5)
BACTRIAN CAMEL — anagram ("changing") of CLIMATE BAN CAR
8 As Aladdin rubs his lamp, the contents turn to fire (4)
BURN — hidden ("contents") backwards (turn) in "Aladdi[N RUB]s"
9 CBBC hit is a calculated insult to woman of conventional tastes (5,5)
BASIC BITCH — anagram ("calculated") of CBBC HIT IS A
10 "Hello, sadness" with internal expression of resignation (2,4)
OH WELL — W ("with") in ("internal") anagram ("sadness") of HELLO.
11 Moving, for old woman confined to bed, is a wrench (8)
CROWFOOT — anagram ("moving") of FOR O(ld) W(oman) inside COT ("bed")
12 Separatist beer-drinking rifle association lady ignoring odds (9)
BREAKAWAY — AK (Kalashnikov, "rifle") + A ("association") in BREW ("beer")
+ (l)A(d)Y ("ignoring odds")
14 Ultimate goal: a success at finals (4)
LAST — last letters ("finals") of (goa)L A (succes)S (a)T
15 Not strong on amusement parks - throws up (4)
AIRS — (f)AIRS ("amusement parks") without F (forte, "strong" in music)
16 Pillowcases and sheets for men Spooner is executing (9)
BEHEADING — Spoonerism of HE BEDDING ("pillowcases and sheets for men")
20 Chase, and sow chaos into demonstration (8)
SHOWCASE — anagram ("chaos") of CHASE SOW
21 Prison riots make one mad (6)
PRIONS (neurally harmful proteins) — anagram ("riot") of PRISON
23 Break-in is from raging infernos (10)
FIRESTORMS — REST ("break") inside anagram ("raging") of IS FROM
24 Suggestion from bride and groom (4)
IDEA — hidden ("from") in "br[IDE A]nd"
25 Perhaps Egyptian I'd led astray with high teas will stop me joining navy (6,7)
MIDDLE EASTERN — anagram ("astray") of ID LED
+ anagram ("high") of TEAS, both inside ("stop") ME + RN (Royal Navy)
Down
1 Makeup would be more vibrant without foundation from Boots (7)
BLUSHER — B(oots) + LUSHER ("more vibrant")
2 Rigged ocean vessel (5)
CANOE — anagram ("rigged") of OCEAN
3 Buller is ravaged by a disease (7)
RUBELLA — anagram ("is ravaged"9 of BULLER + A
4 Get-together with a measure of deviation surpassed by bachelors (9,6)
ASSOCIATE DEGREE — ASSOCIATE ("get together")
+ DEGREE ("measure of deviation", i.e. for angles)
5 Regarding Chanel's first rust-proof coat (6)
COCOON — COCO ("Chanel is first") + ON ("regarding")
6 German woman and German man described first type of crime (4,5)
MAIL FRAUD — homophone ("described") of MALE ("man")
+ FRAU (German for woman) + D (deutsch, "German")
7 Leave work, head off strike by management (7)
LOCKOUT — (c)LOCK OUT ("leave work" without its head)
13 Point to Archers cast who are regularly barred (9)
ARROWHEAD — anagram ("cast") of WHO ARE (b)A(r)R(e)D ("regularly")
15 Dawkins' profession upset his mate (7)
ATHEISM (as described in "The God Delusion" by Richard Dawkins)
— anagram ("upset") of HIS MATE
17 Reveals Canadian team recruiting wingers from Singapore (7)
EXPOSES — S(ingapor)E ("Wingers", i.e. outer letters)
inside ("recruiting") former Montreal baseball team EXPOS
18 Enthusiastic to the end, granny gets fabric (7)
NANKEEN — NAN ("granny") + KEEN ("enthusiastic")
19 Lady Gaga caught going in with fingers (6)
DACTYL ("finger" in Greek) — CT ("caught") inside anagram ("gaga") of LADY
22 Is the centre of Raetihi coming up? You could ask here (1-4)
I-SITE (a visitor information centre in NZ)
— IS + reverse ("coming up") of ra(ETI)hi ("centre of")
