Across:
1 Rugged (ROBUST) bust or (bust or) sculpture (= anagram indicator) (bust or = ROBUST),
4 Great shot locally (locally, great shot/ball = SCREAMER) of Bellow (bellow = SCREAM-) by Ward (-ER) (SCREAMER),
9 House of Lords leader’s (‘House Of Lords’ leaders = HOL-) party (Democratic Unionist Party = -D-UP) (HOLD-UP) offering to delay (HOLD-UP),
10 Miss (-LOSE-) first train (first ‘Train’ = -T-) in Clare (C-E-) going to Dublin (-D) (CLOSETED), as shut up in private meeting (CLOSETED),
12 A (A-) mountaintop of (‘Mountain’ top = -M-) heather (-ERICA-) leads to natural spring (leads to ‘Natural Spring’ = -NS) (AMERICANS) coming from Wyoming, for example (AMERICANS),
13 What one who’s good on their feet might be doing (TANGO) in Spartan government (in ‘sparTAN GOvernment’ = TANGO),
14 Race (STEEPLECHASE) to pursue (-CHASE) the point of The Church (STEEPLE-), from the start (= position indicator) (STEEPLECHASE),
18 Nearly all of those in 8 down (nearly all ‘radios’ = RADIO-) and The Cure (-THERAPY) (RADIOTHERAPY) produced a treatment synonymous with The Waves (RADIOTHERAPY),
21 Demand (EXACT) for DIRT from Direct Tax (‘DIRT’ from ‘Direct Tax’ = ectax = EXACT),
22 Ignore old (ignore old) boss (= anagram indicator) (ignore old = GONDOLIER) working around Rialto (GONDOLIER working around Rialto, Venice),
24 Is it better (SUPERIOR) to rise up or (rise up or) run? (= anagram indicator) (rise up or = SUPERIOR),
25 Get going without it (‘get going’ without ‘it’ = gegong = EGGNOG) for Christmas drink (EGGNOG),
26 Did an about turn (WITHDREW) as comedian (WIT-) on drugs (heroin = -H-) painted a picture (-DREW) (WITHDREW),
27 A lot dumped by intolerant (‘a lot’ dumped by ‘intolerant’ = INTERN) apprentice (INTERN).
Down:
1 Check your lines in advance (REHEARSE) for catches (-HEARS-) in lough (Lough RE-E) (REHEARSE),
2 Turns up (= reverse indicator) Old Nick (devil = -LI-VED) consumes Oriental (east = -E-) starters of Eggs Benedict? (starters of ‘Eggs Benedict’ = EB = BE-) (BELIEVED) Thought so! (BELIEVED),
3 Asian (SAUDI) holds up (= reverse indicator) papers (ID = -DI) by university (-U-) leaders of advisory service (leaders of ‘Advisory Service’ = AS = SA-) (SAUDI),
5 What The Boss does (CALLS THE TUNE) with requests (CALLS) for Born in the USA, for example (THE TUNE) (CALLS THE TUNE),
6 Wild (= anagram indicator) yeast (yeast = EASY T -) and a fair amount of (half of) the pasta flour (half of ‘00’ flour = -O) on view (SEE) (EASY TO SEE) is staring one in the face (EASY TO SEE),
7 Scatter (= anagram indicator) mint (mint = M-TIN-) over top of unremarkable (top of ‘Unremarkable’ = -U-) yard (-Y) (MUTINY) – with the right force, it’ll take over (MUTINY),
8 Queen (Regina = R-) say this in farewell to Barcelona (Spanish ‘adios’ = -ADIOS) (RADIOS) as they’re playing the latest tunes for the listeners (RADIOS),
11 Bar (WATERING HOLE) for Oasis? (WATERING HOLE),
15 Cover job (PLASTER-) for journalist (-ED) (PLASTERED) under the influence? (drunk = PLASTERED),
16 Difference (VARIANCE) in volume (V-) from the magic flute (from Mozart’s The Magic Flute = -ARIA-) in the back of (‘iN’ the back of = -N-) church (Church of England = -CE) (VARIANCE),
17 Some of the water (HYRDOGEN + oxygen = water) on the top of the table is the first one you’ll see (on the top of the Periodic Table, HYDROGEN is No 1),
19 Go back and forth (SEESAW) with energy (-E-) in choppy (= anagram indicator) seas (seas = SE-SA-) approaching start of winter (start of ‘Winter’ = -W) (SEESAW),
20 Jaguar (CAR-) cat (-PET) (CARPET) in ground cover (CARPET),
23 Mouthpiece (ORGAN) heading off (m) on horse (Morgan horse) (m) (‘morgan’ without ‘m’ = ORGAN).