Thank you to Anto. Definitions are underlined in the clues.
Across
1. Check appearance for president (5)
CHAIR : CH(abbrev. for “check” in chess notation) + AIR(appearance/impression given).
Defn: The person who has the highest authority in an organisation, ie. one who presides over.
4. Avoid part of process on border (8)
SIDESTEP : STEP(one/part of a series that constitutes a process) placed after(on) SIDE(edge/border).
8. Every one gathered with present get invitation to join in (3,8,3)
ALL TOGETHER NOW : ALL(everyone) + TOGETHER(gathered/assembled as one) + NOW(the present time).
Defn: … in, say, a singalong.
10. Is it ok to ask for a repeat? (4,4)
HOW’S THAT? : Double defn: 1st: Question seeking confirmation that something is right/ok; and 2nd: Question asking for a repeat/clarification of what has been said.
11. Relaxed as Republican enters a challenge (2,4)
AT REST : R(abbrev. for a member of the Republican Party) contained in(enters) [A TEST](the process of determining, say, the validity of something/a challenge).
12. Carrying off a second rate set of pipes (9)
ABDUCTING : A + B(the second highest grade in a series/second rate) + DUCTING(a set of pipes carrying liquid or gas/ducts).
Defn: … by force or cunning.
15. Exaggerate large raise (3,2)
BIG UP : BIG(large) + UP(to increase/raise).
Defn: Slang for to …/pump up the importance of a person, thing or oneself.
17. Dispute arrest (3-2)
RUN-IN : [RUN IN](to arrest/take into custody).
Defn: …/disagreement with someone.
18. Piglet had disrupted aircraft’s landing approach (5,4)
GLIDE PATH : Anagram of(… disrupted) PIGLET HAD.
Picture the pilot seeing a piglet right in the middle of the runway.
19. Almost cry out during festival – it obscures your vision (6)
EYELID : Last letter deleted from(Almost) “yell”(cry out loudly) contained in(during) EID(a Muslim festival).
21. Holiday cancelled? You must be joking (5,3)
LEAVE OFF : LEAVE(holiday/a break from work) + OFF(not available/cancelled).
Defn: An expression similar to “…”, said in response to something unbelievable or unreasonable that somebody says, and thus telling that somebody to stop pursuing the subject.
24. Call after date – it’s a sign of serious commitment (10,4)
ENGAGEMENT RING : RING(to call, say, on the phone) placed after(after) ENGAGEMENT(a date/an appointment).
25. Deck boss turned out in nightwear (8)
BEDSOCKS : Anagram of(… turned out) DECK BOSS.
26. Tart ironically described like this on menu (5)
SWEET : A taste that is drastically different from tart/an acidic taste, and also, ironically, that section on a menu under which a tart/an open-faced pastry is described.
Down
1. Spooner lecturing arrogant airline – it can reduce accidents (5,7)
CRASH BARRIER : Spoonerism of(Spooner lecturing) [ “brash”(arrogant/offensively bold) “carrier”(an airline) ].

2. Admitted a lone wild drunk (7,2)
ALLOWED IN : Anagram of(… drunk) A LONE WILD.
3. Southern part of base provides resting area (5)
ROOST : S(abbrev. for “southern”) contained in(part of) ROOT(the base/bottom-most part).

4. Notice cutting type of irresolute behaviour (3-6)
SEE-SAWING : SEE(to notice/perceive) + SAWING(cutting with a back and forth motion, with a saw or other tool).
5. Half of dons hate city (4)
DOHA : 1st 2 out of 4 letters, respectively, of(Half of) “dons hate”.
Answer: Capital city of Qatar.
6. Easy to read report of cheat on board (9)
SCRUTABLE : Homophone of(report of) “screw”(to cheat/to con someone) plus(on) TABLE(the food that is served/board).
7. Weirdo’s diet regularly includes crumble (5)
ERODE : 2nd and every other letter thereafter of(… regularly) “Weirdo’s diet”.
9. Finish quarrel by counting to ten? (4,3,5)
STOP THE FIGHT : Cryptic defn: Refering to what the referee in a boxing match/fight does after he/she has counted out (from 1 to 10) the boxer who has been knocked down.
13. Writer blocking waterways? They’ll have him for breakfast (9)
CANNIBALS : NIB(the pointed writing tip of a pen, and therefore a writer) contained in(blocking) CANALS(waterways/man-made water channel).
Defn: …, ie. they’ll eat the writer/author.
14. I see gulls circling? That’s natural (9)
GUILELESS : Anagram of(… circling) I SEE GULLS.
Defn: …/innocent/artless.
16. Add some sparkle to gem sailor messed with (9)
GLAMORISE : Anagram of(… messed with) GEM SAILOR.
20. Wise man spots current in Irish river (5)
ERNIE : I(symbol for electric current in physics) contained in(in) ERNE(a river in Ireland).
Answer: … Wise, half of the comic duo, Morecambe and Wise.
22. Partially apologise to Vatican over ballots (5)
VOTES : Hidden in(Partially) reversal of(…. over) “apologise to Vatican”.
23. Starts to manufacture exceptionally reliable cable car (4)
MERC : 1st letters, respectively, of(Starts to) “manufacture exceptionally reliable cable”.
Answer: Slang name for a Mercedes Benz car.
Good fun after yesterday’s Pangakupu “challenge”. I haven’t heard of the expression BIG UP. My knowledge of boxing was insufficient to parse STOP THE FIGHT, and I didn’t think of Ernie Wise (and didn’t know the Irish river). I thought at first that sage might have somehow had something to do with it.
Enjoyed your pictorial, scchua, as always.