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.