Thank you to Filbert. Definitions are underlined in the clues.
Across
1. Jargon I allow, having talked turkey first (12)
GOBBLEDEGOOK : GOBBLED(made a swallowing sound characteristic of a turkey/having talked turkey) placed before(first) EGO(a person’s self-image/ego) + OK(or “okay”/to give the go-ahead/to allow).
Defn: …/language made unintelligible by excessive use of technical terms.
9. Cut off in long twisted pieces (8)
STRANDED : Double defn: 1st: …/left abandoned and unable to move; and 2nd: …/made of long thing lengths of, say, thread or fibre, twisted around each other.
10. Thingamy‘s party none enjoyed, on reflection (6)
DOODAH : DO(a party/a social function) + O(letter representing 0/nothing) + reversal of(…, on reflection) HAD(experienced/enjoyed).
Defn: …/something that one cannot name precisely.
11. What about rolls for hunger? (4)
ACHE : Reversal of(… rolls) [ EH?(like “what?”, an expression of enquiry) + CA(abbrev. for “circa”/about when used in reference to time periods, eg. years) ].
Defn: …/desire.
12. Child eating seconds of steak made our bull cross (8)
MINOTAUR : MINOR(one who has not reached the age of full legal responsibility/a child) containing(eating) 2nd letters, respectively, of(seconds of) “steak made our”.
Answer: A mythical Greek creature that is a composite/a cross of the head of a bull and the body of a man.
14. Peril Cuba largely represented as one of USSR’s vassals (8)
REPUBLIC : Anagram of(… represented) [PERIL + “Cuba” minus its last letter(largely) ].
Defn: …/one of the socialist republics in the former Union of Soviet Socialist Republics.
15. Perfect decider at Wembley netted close to time (6)
REFINE : REF(short for “referee”, whom you might call a decider/arbitrator in a football match in Wembley Stadium, London) + IN(short for “in the net” or “in the goal”/netted in a sport like football) + last letter of(close to) “time“.
Defn: To …/to make free of defects or mistakes.
17. Deep void right inside Vance spread (6)
CAVERN : R(abbrev. for “right”) contained in(inside) anagram of(… spread) VANCE.
19. Rest in Leeds, travelling south (8)
IDLENESS : Anagram of(…, travelling) IN LEEDS + S(abbrev. for “south”).
21. Successfully jump over high bunk (5,3)
CLEAR OFF : CLEAR(to successfully/safely jump over a raised obstacle, say, a hurdle) + OFF(rotting/high).
Defn: To …/to go away.
23. Event with games and refreshments cost hosts time (4)
FETE : FEE(the cost for a service rendered) containing(hosts) T(abbrev. for “time”).
25. Quite violent equestrian events in which Oscar comes last (4,2)
JUST SO : JOUSTS(medieval sporting contests in which two opposing horse riders fought with lances/violent equestrian events) with O(letter represented by “Oscar” in the phonetic alphabet) moved to the end(in which … comes last).
Defn: Like …, an expression of agreement.
26. Likely Republican gets overwhelming ovation for silly speech (8)
CLAPTRAP : [ APT(having the tendency to do a specified something/likely) + R(abbrev. for a member of the Republican Party) ] contained in(gets overwhelming) CLAP(show of approval by the clapping of hands/ovation).
27. Poor saint behind tree shat trousers (4-8)
CASH-STRAPPED : [ ST(abbrev. for “Saint”) placed after(behind) ASH(one of a genus of trees) ] contained in(… trousers) CRAPPED(discharged shit/shat).
Down
2. Shock from back of generator during power cut (7)
OUTRAGE : Last letter of(back of) “generator” contained in(during) OUTAGE(a period when power supply is unavailable/a power cut).
3. American in Soho, tube heaving, gets home for eight (9)
BOATHOUSE : A(abbrev. for “American”) contained in(in) anagram of(… heaving) SOHO, TUBE.
Defn: …, that is, for an eight-oared rowing boat.
4. Vortex that inspired Dyson hoovers? (4)
EDDY : Hidden in(… hoovers/sucks up) “inspired Dyson”.

5. Venice exposed with rising sea coming in across the region (7)
ENDEMIC : “Venice” minus its 1st and last letters(exposed) containing(with … coming in) reversal of(rising, in a down clue) MED(short for the Mediterranean Sea).
Defn: Describing, say, a disease that regularly occurs within and across that particular region.
6. Arab’s cash I brought through Paris airport as usual (10)
ORDINARILY : [ DINAR(unit of currency/cash in some Middle Eastern/Arab countries) + I ] contained in(brought through) ORLY9one of the Paris airports).
7. Russian scourge treating UK to a bit of Novichok (5)
KNOUT : Anagram of(treating) [ UK TO + 1st letter of(a bit of) “Novichok” ].
Defn: …/whip used in imperial Russia to inflict punishment.
8. World leaders that shout and argue have become sour (6)
SATURN : 1st letters, respectively, of(leaders that ?) [ “shout” plus(and) “argue” ] plus(have) TURN(to become sour, said of milk/to curdle).
Defn: …/another heavenly body, like Planet Earth is.
13. Noisy family? Try ours for a change (10)
CLANGOROUS : CLAN(a large extended family) + GO(a try/an attempt at doing something) + anagram of(… for a change) OURS.
16. Better advice about golf which might fetch you a bogey (9)
FINGERTIP : [ FINER(better/of a higher quality) + TIP(a small and useful piece of advice) ] containing(about) G(letter represented by “golf” in the phonetic alphabet).
Defn: If you dig your nose, that …, a piece of nasal mucus, that is.
18. Extremely hard for ten playing cricket (3-3)
ALL-OUT : [ALL OUT](in cricket, signifying the end of an innings, when 10 out of 11 batsmen have been dismissed).
Defn: …/using maximum effort.
19. Sharp intelligence of copper (2,5)
IN FOCUS : INFO(short for information, in this case info of military or political value/intelligence) + CU(symbol for the chemical element, copper) + …‘S(denoting possession/belonging to/of).
20. Leaf on the end of twig oozing (7)
SEEPAGE : PAGE(a leaf/a single sheet of paper, in a book, say) placed after(on the end of) SEE(to grasp the meaning of/to twig).
Defn: …, as a noun.
22. Lorry starts to alarm rider with uncontrolled movement (5)
ARTIC : 1st letters, respectively, of(starts to) “alarm rider” plus(with) TIC(involuntary muscle spasm/uncontrolled movement).
Defn: Short for an “articulated lorry”, one with two or more sections connected by a flexible joint.
Too much flexibility?:

24. Pretty remote island is splitting (4)
FAIR : FAR(remote/in the middle of nowhere) containing(… is splitting) I(abbrev. for “island”).
Filbert in the Sunday morning slot and all is right in my world. Not as tricky as he can be but as enjoyable as always. CASH-STRAPPED and STRANDED among my favourites. Early blog nice for antipodeans. Thanks schuaa and Filbert.