Across
Ruler against stopping progress (7)
Described little bear following father home (7)
Members of people's party held back in recess (4)
Arrows men shot defending a Trojan vehicle? (10)
I haven't cracked this one yet — but Fifteensquared have:
Arrow’s men shot defending a Trojan vehicle A in *(ARROW’S MEN); “shot” is anagram indicator; the Trojan of the definition is the ostensibly helpful, but in reality harmful, computer software
Cretan lied appallingly in testimony (10)
Rector leaves obese woman (4)
Fellers taking the lead from those who sleep (9)
I haven't cracked this one yet — but Fifteensquared have:
Fellers taking the lead from those who sleep <s> LUMBERERS (=those who sleep); “taking the lead from” means first letter is dropped; the “fellers” of the definition are people who fell trees!
Pursuit of raptor (5)
Weary maiden returns showing virtue (5)
Grown-ups welcoming article defending soldiers and lackeys? (9)
I haven't cracked this one yet — but Fifteensquared have:
Grown-ups welcoming article defending soldiers and lackeys ? OR (=soldiers, i.e. Other ranks) in [A (=article, in grammar) in ADULTS (=grown-ups)]; adulators are hopeless admirers, servile followers, hence “lackeys”
Information Faraday omitted in book (4)
I haven't cracked this one yet — but Fifteensquared have:
Information Faraday omitted in book <f> ACTS (=information, data); “ Faraday (=F, unit used in electrolysis) omitted” means letter “f” is dropped; the Acts of the Apostles is the fifth book of the New Testament
Supervisor has to punish footballer (10)
Introduction of setter's site (10)
I haven't cracked this one yet — but Fifteensquared have:
Introduction of setter’s site I’M (=setter’s, i.e. Kairos’s) + POSITION (=site); the imposition of new rules, say, is their introduction
New Orleans working time (4)
Port and beer imbibed by priest and doctor (7)
I haven't cracked this one yet — but Fifteensquared have:
Port and beer imbibed by priest and doctor [ALE (=beer) in PR. (=priest)] + MO (=doctor, i.e. Medical Officer); Palermo is a port and the capital of Sicily
Notice star left Nelson? (7)
Down
Suitable work left with one in France (9)
Element to stop change (5)
Judge’s expression of surprise over expert (7)
God's a cut above ordinary (6)
Slope went awry in part of stairs (9)
Offended by earls entertaining bishop and duke (5)
I haven't cracked this one yet — but Fifteensquared have:
Offended by earls entertaining bishop and duke [RR (=bishop, i.e. Right Reverend) in E E (=earls, i.e. 2 x E=earl)] + D (=duke)
Against Jude and others employed by Claude? (4)
Sulphur and bromine site regularly mixed (9)
I haven't cracked this one yet — but Fifteensquared have:
Sulphur and bromine site regularly mixed *(BROMINE + S <i> T <e>); “regularly” means alternate letters only are used in anagram, indicated by “mixed”
Age of Father Abraham (3)
Reportedly claim small amount of money (3)
I haven't cracked this one yet — but Fifteensquared have:
Reportedly claim small amount of money Homophone (“reportedly”) of “sue (=claim, to make a legal claim)”
Ben and Carol composed a musical number (9)
I haven't cracked this one yet — but Fifteensquared have:
Ben and Carol composed a musical number *(BEN + CAROL) + A; “composed” is anagram indicator; Barcelona could be the 1987 song by Freddie Mercury and Montserrat Caballé, or the song in the 1970 Stephen Sondheim musical Company .
Made a comparison with light surrounding president Nixon's head (7)
I haven't cracked this one yet — but Fifteensquared have:
Made a comparison with light surrounding President Nixon’s head [IKE (=President, i.e. Eisenhower) + N <ixon> (“head” means first letter only)] in LED (=light, i.e. light-emitting diode)
Say order preserves island's self-interest (6)
Smallest division of winged insect (5)
I haven't cracked this one yet — but Fifteensquared have:
Smallest division // of winged insect Double definition: a comma marks the “smallest division” of a sentence AND is a type of butterfly, hence “winged insect”
Work with cut linen (4)
I haven't cracked this one yet — but Fifteensquared have:
Work with cut linen TOIL <e> (=linen, i.e. dress material); “cut” means last letter is dropped
Boredom of sister cycling in East India (5)
I haven't cracked this one yet — but Fifteensquared have:
Boredom of sister cycling in East India NNU (NU N =sister; “cycling” means last letter moves to front of word) in [E (=East) + I (=India, in NATO alphabet)]
Type letters or click words in the clue