Across
Empty diary to accommodate private sector event (6,5)
I haven't cracked this one yet — but Times for the Times have:
Remove the contents of D[iar]Y and replace with INNER for private and PART for sector.
Animal jumping two ducks on river (3)
I haven't cracked this one yet — but Times for the Times have:
From Down Under, of course. Two 0’s (a duck in cricket is a zero score) place on R[iver].
Agreeable notes written about clubs inside paved area (9)
I haven't cracked this one yet — but Times for the Times have:
The note to pluralise and then reverse (written about) is MI, then add C[lubs] inside PATIO, a paved area. Chambers says it’s “Sympathetic in the sense of congenial” and derives as you might expect from Italian and Spanish
Carefully examining wingless bird (5)
I haven't cracked this one yet — but Times for the Times have:
Carefully examining gives PROBING: clip its PG wings.
Piece involving divine persons in good works? (7)
I haven't cracked this one yet — but Times for the Times have:
A divine is a D[octor of] D[ivinity], add MEN for persons and encase all in O[ld] T[estament], good works in the good book.
Found daughter's left carrying new cloak (7)
I haven't cracked this one yet — but Times for the Times have:
To found is (perhaps a little loosely) to DEVELOP. Knock off the D[aughter] and insert N[ew].
Standard and prow removed from Darwin's ship (5)
I haven't cracked this one yet — but Times for the Times have:
Darwin’s most famous ship was the BEAGLE, remove the front or prow and you have a standard carried by Roman and French armies.
Feeling Irish Republic must shelter no undesirable (4,5)
I haven't cracked this one yet — but Times for the Times have:
I think it’s a bit of a jump from feeling to BET, but one we have to make. Then EIRE the Irish Republic includes NO in plain sight.
In a bizarre sense armed struggle brings enlightenment (9)
I haven't cracked this one yet — but Times for the Times have:
Place WAR for armed conflict inside of an anagram (bizarre) of A SENSE.
Knight stops magician creating beastly inflammation (5)
Resentment in club: first couple missing for days! (7)
I haven't cracked this one yet — but Times for the Times have:
I think this is BLUDGEON for club with its first two (letters) missing and replaced by D(ays). Given the plural days, you can spend time puzzling how to replace two of something with Ds and end up with a U in the middle.
Lovely, large shed for one working land (7)
I haven't cracked this one yet — but Times for the Times have:
A golden oldie, with PLEASANT shedding its L[arge]
Great tragedy to miss out on overtime — anyone there? (5)
I haven't cracked this one yet — but Times for the Times have:
The great tragedy of OTHELLO loses its O[ver]T[ime.
Instrument to cut branches? Sharpen axes first (9)
I haven't cracked this one yet — but Times for the Times have:
LOP is to cut (might as well be) branches. Add HONE for sharpen, then put the X and Y axes from a graph in first place.
Is it Dalyell appearing in Just a Minute? (3)
I haven't cracked this one yet — but Times for the Times have:
Tam Dalyell was a Labour politician of independent mien, who appears for our benefit hidden in Jus T A M inute, which is a long running radio panel game in which comedic contestants attempt to speak for 60 seconds without hesitation, repetition or deviation, with hilarious results (it says on the BBC website). Younger and expat members might find this a little arcane.
Three-page note amended by Yankee offering medical treatment (4,7)
I haven't cracked this one yet — but Times for the Times have:
An anagram of THREE-PAGE plus N[ote] and Y[ankee]
Down
Vicious, perhaps on the rise, an underworld figure (3)
All there in Glasgow for traveller? (5)
Stand from beginning of extra time: add time on (7)
Odd parts in Persian book in story fit to publish (9)
I haven't cracked this one yet — but Times for the Times have:
The odd letters of PeRsIoN, plus B[ook] contained in TALE for story.
Right working for ambassador to collect flower (5)
I haven't cracked this one yet — but Times for the Times have:
After R[ight] you allow H[is] E[xcelency] the ambassador to collect ON for working.
Maintain returns to swell money for capital (7)
I haven't cracked this one yet — but Times for the Times have:
To AVER is to maintain a statement to be true, reverse it a stick it into YEN for money. Yerevan is the capital (city) of Armenia.
Rising hero seen pursuing bishop in lively dance (9)
I haven't cracked this one yet — but Times for the Times have:
Commonly in these things a hero is a LION, here placed after B[ishop] contained by a REEL characterised as a lively dance.
Ubiquitous minestrone soup finally prepared (11)
I haven't cracked this one yet — but Times for the Times have:
A rather satisfying anagram (prepared) of MINESTRONE plus the last letter of [sou]P
Clear riotous thousand mobbing author (4-3-4)
One's achievement having not missed a trick? (5,4)
I haven't cracked this one yet — but Times for the Times have:
Barely cryptic. If you win all 13 tricks in Bridge it’s the result.
Thrown stiletto catches Penny — one up for trial? (4,5)
I haven't cracked this one yet — but Times for the Times have:
A mildly whimsical definition, its answer springing from an anagram (thrown ) of STILETTO plus P[enny]
Melody on radio extended by and by (7)
Nosh very good that feeds the writer: pasty possibly (4,3)
I haven't cracked this one yet — but Times for the Times have:
(To) nosh is to EAT, PI is very good, both are held withing ME the writer.
Nothing doing! (Tricky Dick) (5)
Precious metals area in Greek shopping centre? (5)
I haven't cracked this one yet — but Times for the Times have:
The precious metals are AG for silver and OR for gold. Add A[rea]. the result is an ancient Greek marketplace, among other things.
Bank failing to open in cathedral city (3)
I haven't cracked this one yet — but Times for the Times have:
Not many 3 letter cathedral cities, but its RELY for bank (on) with no first letter.
Type letters or click words in the clue