Across:
1 First goal (first ‘goal’ = G-) leaves a bad smell in the air (-REEKS) (GREEKS) for Ajax and others (GREEKS),
4 Leggy (leggy = EGG Y-L-) model (= anagram indicator) embraced Oscar (-O-) for weekend (‘week’ end = -K-) bender (-S bend) (EGG YOLKS) in Mayo! (EGG YOLKS),
9 Nosey Parker dismisses Karen (‘Nosey Parker’ dismisses ‘Karen’ = oseypr = OSPREY) Hawk (OSPREY),
10 Usual fob (usual fob = FABULOUS) off (= anagram indicator) is beyond the realm of reason (FABULOUS),
12 Carnage (BLOODSHED) in Slaughterhouse? (BLOOD SHED),
13 Light-footed (AGILE) barman (Attorney General = AG-) loses head (f) in row? (row/line = ‘file’ without ‘f’ = -ILE) (AGILE),
14 Most of those in 1 across (most of ‘Greeks’ = GREEK) and 25 across (‘island’ = ISLAND-) go to Sicily’s capital (‘Sicily’s’ capital = -S) (GREEK ISLANDS) in the Mediterranean (GREEK ISLANDS),
18 Contests (COMPETITIONS) this is to keep up with the Joneses (to keep up with the Joneses / the COMPETITION-) at school (-S) (COMPETITIONS),
21 Left (L-) a foreign (a = -UN-) soldier (-GI) (LUNGI) covering up part for body in Burma (sarong / LUNGI),
22 A real open (a real open = AEROPLANE) question (= anagram indicator) for highflyer (AEROPLANE),
24 The caddie is aware of them (YARDAGES), in the school (YARD-), for a long time (-AGES) (YARDAGES),
25 One (I-) school (-S-) near Limerick (-L-) and (-AND) (ISLAND) Clare, for example? (Clare ISLAND),
26 Solitary (solidary = ROYALIST) drunk (= anagram indicator) – a supporter of The Palace (ROYALIST),
27 Made fun of (TEASED) tenor (T-) to reduce the tension (-EASE-) – it’s key (music key -D) (TEASED).
Down:
1 Government (G-) quarrel (-ROW-) leads to bigotry and grudge significantly (leads to ‘bigotry and grudge significantly’ = -BAGS) (GROWBAGS) for the moneymakers in the plots (GROWBAGS for the moneymakers/tomatoes in the plots),
2 Bossy type (EMPLOYER) makes work for others (EMPLOYER),
3 Job handling the dough (KNEAD) in demand (“need” = “KNEAD”) all told (= homophone indicator),
5 One thousand (GRAND-) teachers (-MASTERS) (GRANDMASTERS) are capable of finding their mates really easily (GRANDMASTERS find checkmates really easy),
6 I completely agree (YOU SAID IT) yob briefly (‘yob’ briefly = YO-) goes to America (USA = -U SA-) to one (-I-) college (Dublin Institute of Technology = DIT = -D IT) (YOU SAID IT),
7 Family (kin = -K IN) bathroom (LOO-) opens (= position indicator) (LOOK IN) – check it out (LOOK IN),
8 Rest is (is rest = SISTER) ordered (= anagram indicator) for relative (SISTER),
11 Those in 5 down, for example (‘grandmasters’ = CHESS PLAYERS), responsible for a number of exchanges on the board (CHESS PLAYERS),
15 Present (-NOW-) found in equipment (kit = K- -IT-) is for everyone (-ALL) (KNOW-IT-ALL) with clever clogs (KNOW-IT-ALL),
16 Won (won = NOW-) over (= reverse indicator) a (-A-) relative (-DA-) and youths on both sides (‘youths’ on both sides = -YS) (NOWADAYS) in the current climate (NOWADAYS),
17 Dance (dance = A-CEND-) wildly (= anagram indicator) around Capital Showband (capital Showband = -S-) with Edward (-ED) (ASCENDED) and Rose (rose/went up = ASCENDED),
19 Layperson has no son (‘layperson’ has no ‘son’ = layper = PLAYER) working in the theatre (PLAYER),
20 Primate leaves prayer meeting (‘primate’ leaves ‘prayer meeting’ = yereng = ENERGY) with enthusiasm (ENERGY),
23 No longer fashionable (PASSE) to back off (d) getting one’s exams (passed) (‘passed’ without ‘d’ = PASSE).