Across
Opening of song memorable, capturing hint of recordings such as old 78s? (8)
I haven't cracked this one yet — but Times for the Times have:
S{ong} [opening], CATCHY (memorable) containing [capturing] R{ecordings} [hint of…]. I think we have to take it that ‘such’ refers back to ‘recordings’ in order to avoid any suggestion of double-duty.
Notice breakdown in communication, perhaps, at sea (6)
Unusual slice taken from cut of beef? (3)
I haven't cracked this one yet — but Times for the Times have:
RUM{p} (cut of beef) [slice taken]
I'm brought in to sound loud: hope things will improve? (4,3,4)
I haven't cracked this one yet — but Times for the Times have:
I’M contained by [brought in to] PLAY (sound) + FORTE (loud)
Lady once thrilled to host working author (5,5)
Weary diatribe getting a Democrat removed (4)
I haven't cracked this one yet — but Times for the Times have:
TIR{ad}E (diatribe) [a Democrat removed]
Soft chap, solemn at heart (6)
Way of speaking recalled in time in letter (7)
I haven't cracked this one yet — but Times for the Times have:
LISP (way of speaking) reversed [recalled] contained by [in] EON (time)
An outpouring enshrining one's suffering (7)
I haven't cracked this one yet — but Times for the Times have:
AN, GUSH (outpouring) containing [enshrining] I (one)
Movement of air beginning to bring chill? Not the first (6)
I haven't cracked this one yet — but Times for the Times have:
B{ring} [beginning], {f}REEZE (chill) [not the first]
Not all bits of blossom everywhere (4)
Store opening recalled by the writer in city (10)
I haven't cracked this one yet — but Times for the Times have:
ME (writer), then SILO (grain store) + PORT (opening – aperture) reversed [recalled]
Cautious Mike, enthralled by top entertainment, favoured going round clubs (11)
I haven't cracked this one yet — but Times for the Times have:
M (mike – NATO alphabet) contained [enthralled] by CIRCUS (big top entertainment), then PET (favoured) containing [going round] C (clubs – cards)
Gamble to avoid heading for rocks (3)
I haven't cracked this one yet — but Times for the Times have:
{d}ICE (gamble) [avoid heading]
Dimwit mostly with nothing to say about Oxbridge degree (6)
Individual crime not initiated with sound of bell around (8)
Down
Smart player finally participating in European trophies after reflection (6)
I haven't cracked this one yet — but Times for the Times have:
{playe}R (finally) contained by [participating in] E (European) + CUPS (trophies) reversed [after reflection]
Catholic married to Anglican? It's a wonderful story (7)
Prepare for cooking a plant — do it with mincing? (3,3,4)
Completely taken by alphabetical statement of the obvious? (4,4,5)
Choice of Roman numerals to indicate sleeping quarters (4)
I haven't cracked this one yet — but Times for the Times have:
D OR M (choice of Roman numerals)
Opening popular with one chess champion going round India (7)
I haven't cracked this one yet — but Times for the Times have:
IN (popular), I (one), then TAL (World chess champion – Mikhail) containing [going round] I (India – NATO alphabet)
Historic city ultimately ignored by an old pictorial publication (3,5)
I haven't cracked this one yet — but Times for the Times have:
THEBE{s} (historic city) [ultimately ignored], AN, O (old). The Beano comic was not the first publication to come to mind, but was none the less very welcome when found to be what was required.
Risqué theatre possibly giving ogler freebies (6,7)
They treat bones and muscles — doctoring to the psoas? (10)
Top music broadcast — one of the Chili Peppers? (8)
Hesitation over doctor in Republican party providing candy? (7)
I haven't cracked this one yet — but Times for the Times have:
UM (hesitation) + DR (doctor) contained by [in] GOP (Republican party – Grand Old Party)
Elizabeth, upcoming celebrity, an unknown quantity (7)
A distended shape to boot (2,4)
Zero employment current in York (4)
Type letters or click words in the clue