2 down: Dug light drink carrier (3, 4)
I figured this was tea tray, but I had no idea why dug = teat. A dictionary told me, though, that dug is exactly a teat as well as being related to a shovel.
7 down: Barge equestrian champ (3)
Here, barge = hoy = equestrian champ (as in Andrew Hoy, the Olympic gold medallist). Until I looked it up, I had no idea barge = hoy.
13 across: …stars in carbon-free cycle wear (4)
This one was guessable with cycle wear = lycra so that carbon-free cycle wear = lyra = stars. And with that, I learnt a new constellation.
16 across: Woeful line with PC-adapted tool for editing (4, 6)
We’ve got woeful = blue and line with PC-adapted = pencil so that woeful line with PC-adapted = blue pencil = tool for editing. What I had no idea of was that a blue pencil is customarily used for editing.
19 across: How rappers welcome politico slog? (4)
How rappers welcome = yo and politico = mp, but who knew before doing this crossword that yomp is slang for slog?
17 down: Leaner dog breed?! (7)
Leaner = lurcher = dog breed. What I didn’t know is that a lurcher is a crossbred dog.
26 across: Headlined feature: High Water Repelled Vermin (5, 3)
RC, in his guise as a well-travelled geographer, came out with tarn as a small mountain lake, which I had never heard of. With that, we had ourselves the following explanation: headlined feature = brow and high water = tarn gave headlined feature: High Water Repelled = brown rat = vermin.
Update: Now that I know how the following clue works, thanks to AL, I’ve got another teaching to list:
21 across: Savage dog returns about mating period (6)
Dog = lab and mating period = rut (which was news to me), which gives dog returns about mating period = brutal = savage.