Thank you to Filbert. Definitions are underlined in the clues.
Across
1. Band tour on back of success on-line? (6)
STRIPE : TRIP(a tour/journey) placed after(on) last letter of(back of) “success” + E-(prefix to denote something to be found online/available on the internet).
4. Propose splitting amount that’s coughed up (6)
SPUTUM : PUT(or put forward/to propose) contained in(splitting) SUM(the total amount).
Defn: That substance which is coughed up.
9. Sheep anti/pro low cloud (10)
CONFORMIST : CON(against/anti) + FOR(pro/supporting) + MIST(low/near-the-earth’s-surface cloud).
Defn: …, figuratively/a follower who totally complies with the group’s norms.
10. Backing lost for nosy US agency (4)
NASA : Last letter deleted from(Backing lost for) “nasal”(relating to the nose or what you might term “nosy” a la water/watery).
Answer: …, the National Aeronautics and Space Administration.
11. Gay in Ghent so upset there are no bars (8,4)
ANYTHING GOES : Anagram of(… upset) GAY IN GHENT SO.
Defn: …, ie. nothing is disallowed/barred.
13. Protruding part goddess squeezes back in (6)
HERNIA : HERA(in Greek mythology, the highest ranking goddess) containing(squeezes) reversal of(back) IN.
Defn: … in the body where an internal organ pushes through surrounding muscle or tissue wall.
14. Explosive combat involved great sacrifice (8)
HECATOMB : HE(abbrev. for “high explosive”) + anagram of(… involved) COMBAT.
Answer: An ancient Greek or Roman religious sacrifice of one hundred cattle to the gods.
16. Five plus Burgess, say, turned communist once (8)
YUGOSLAV : Reversal of(…, turned) [ V(Roman numeral for “five”) + ALSO(plus/in addition) + GUY(an example/say, of one with the last name Burgess, who was a double agent for the Soviets – one who turned communist) ].
Defn: One who belonged to a former/once Soviet Republic.
18. Somewhat peculiar man in expensive clothes (6)
ARMANI : Hidden in(Somewhat) “peculiar man in”.
Defn: Symbolic of ….
20. Walter fixes shoes for Spooner’s runs (12)
COLLYWOBBLES : Spoonerism of (Spooner’s) [ “wally”(short form of the name, Walter) “cobbles”(fixes shoes as a cobbler does) ].
Answer: Slang for “acute diarrhoea”/the runs.
23. Tool store (4)
FILE : Double defn: 2nd: … a digital record on a computer or a paper document in a folder.
24. US cop that is blocking tunnel at ground (10)
LIEUTENANT : IE(abbrev. for “id est”/that is) contained in(blocking) anagram of(… ground) TUNNEL AT.
Defn: One of the ranks in a US police force.
25. Cry quietly having dispatched one large lemon? (6)
YELLOW : YELL(to cry loudly/shout) + “low”(at a low volume/quietly) minus an(having dispatched one) “l”(abbrev. for “large”).
Defn: The colour, ….
26. Stimulating stuff from lead characters in naughty novel, I’m told (6)
ENZYME : Homophone of(… told) [ “ens”(written form of the 1st letters/lead characters in “naughty” and “novel”) + “I’m” ].
Defn: …, ie. compounds that speed chemical changes in the body.
Down
1. Break crockery up (4)
STOP : Reversal of(… up, in a down clue) POTS(round vessels for cooking food/crockery).
Defn: …/pause.
2. Those stopping football and cricket desist (7)
REFRAIN : REF(or referee, one who has the authority to stop play in a football match) + RAIN(weather that will stop a cricket match from continuing).
Defn: …/hold back from doing an action.
3. Maybe Labour overturned Liberal legislation’s divisive feature (5,4)
PARTY WALL : PARTY(an example of which/maybe is the Labour Party) + reversal of(overturned) [ L(abbrev. for a member of the Liberal Party) + LAW(a rule created by a legislative body/a legislation) ].
Defn: … standing between two landed properties or apartments.
5. Advice from below about where to fix rope (5)
PITON : Reversal of(… from below) TIP(a helpful piece of advice) + ON(concerning/about, as in “the talk was on taxation”).
Defn: … when mountain climbing:

6. Stretched nurses down for shifts this evening (7)
TONIGHT : TIGHT(stretched/taut) containing(nurses) ON(scheduled to work during specific time periods/down for shifts).
7. Chief planner furious about M1, forbidding bridges (10)
MASTERMIND : MAD(furious/very angry) containing(about) [MI(M1 with the Roman numeral substitution for “one”) contained in(… bridges/goes over) STERN(showing disapproval/forbidding)].
8. Drone maybe brought into harbour after power failure (5-4-4)
MIGHT-HAVE-BEEN : [ BEE(the male of which is a drone) contained in(brought into) HAVEN(a harbour/a safe place in which to shelter) ] placed after(after) MIGHT(power/strength).
12. Shapelessness misrepresented by outlines (10)
NEBULOSITY : Anagram of(misrepresented) BY OUTLINES.
15. Fake tea the French turn brown (9)
CHARLATAN : CHAR(slang for tea, the drink) + LA(the article “the” in French) + TAN(to turn brown in skin tone, after being in the sun).
17. Fuel supply cook uncapped successfully (3,4)
OIL WELL : “boil”(to cook in boiling water) minus its 1st letter(uncapped, in a down clue) + WELL(with a satisfactory result/successfully).

19. Building work that near bores old PM (7)
MASONRY : [ SO(“that” as in “I want to do it like so/that” or “You say I was there? So/That I was”) + NR(abbrev. for “near”) ] contained in(bores) MAY(Theresa, former/old UK PM).
21. OK without sealing airlock regularly (5)
WILCO : WO(abbrev. for “without”) containing(sealing) 2nd, 4th and 6th letters of(… regularly) “airlock”.
Answer: In radio or military communication, short for “will comply”/OK.
22. Somebody catching cold at any time (4)
ONCE : ONE(pronoun used to refer to a person/somebody) containing(catching) C(abbrev. for “cold”).
Answer: As in “Call me once/at any time/whenever it happens”.
The blog does not mention the ‘r’ in CHARLATAN. I had ‘char’ as an informal British word for tea, as in ‘char wallah’. Enjoyed the puzzle. Thanks.
sofamore, you’re right. Blog corrected.
Seems that tea can be cha/r, with or without, whereas cleaner is always char. Cruisy job, tho I missed parsing the two ‘enz’, dim! Thanks Filbert and scchua.