Most kind!

Another name starts adding luxury in another sense (5)

alias (first letters of adding luxury in another sense)

A belt by any other name looks just as good! ===[**CDM**]===

Thanks much, Rog!

Fish beginning to gobble up tarts (7)

Direct on the left. 3 vowels.

Wordplay = 1 + 2 + 4
cvccvvc

Guppies

That's it, Koala! ===[**CDM**]===

Many Thanks Sherlock.

Iron and wood carrier (6)

Clues huh?

1. Direct on right
2. 3 vowels (all different)
3. 3 consonants (not all different)
4. One of the aforementioned vowels is an 'e'

Bonus clue: No 'f'

I think this must be caddie, being a carrier for golf clubs (iron and wood), although as a non-golfer it took me a while to make the connection

You scored a hole-in-one there Lex.

===[**CDM**]===

Thank you Mr K!

Racecourse built somewhere in Paris (5,5)

Direct on the right cvccv cvvvc

Aha! A good old anagram -> Sacre couer

Correct good sir, allowing for the typo in Coeur

Voici La Ceinture ===[**CDM**]===

...which reminds me of this song https://www.youtube.com/watch?v=MLUaV02Eo5s

Thank you kind sir! To paraphrase Eric Morecombe - "I've got the right letters, but not necessarily in the right order"

Must admit I hadn't come across Mr Allwright...

Sun god returns coins left for messenger (9)

ar/change/l

I only know of Graeme Allright as a result of a year in Paris as a student at a time when Leonard Cohen was a strong influence on French musicians, the main other one I recall being this https://www.youtube.com/watch?v=CyeQ2F6Ja1w
...although Serge Gainsbourg, Charles Aznavour and Johnny Hallyday also loomed large - Easy Rider was a film of the moment and its soundtrack was very popular there

... but in the here and now someone steered me towards Allison Russell which took me to Birds of Chicago https://www.youtube.com/watch?v=RA1L_GvwiG4
and https://www.youtube.com/watch?v=pvEERoYYz50 and thence to Mark Heard (previously unknown to me)
https://www.amazon.com/Treasure-Broken-Land-Songs-Heard/dp/B06Y5W9R87 - all very cool stuff even if I am somewhat hi-jacking my own thread...!

Will dive into them, Lex...

Cheryl, a messenger approaches bearing gifts ===[**CDM**]===

Thanks, Rog!

Stuck with bad, bad bets (7)

Direct on left. 2 vowels.

Stabbed = stuck - anagram (bad) of bad bets

I guess you're stuck with this, Lex! ===[**CDM**]===

Thank you: as it happens, stuck with a very dodgy internet connection for the last few days...

He's investigating every tape I edited (7,3)