Heyer decoded

‘You won’t mind if I shake the fidgets out of his legs!’ Sophy called. ‘He is itching for a gallop!’

With that, she wheeled Salamanca about, and let him have his head down the stretch of tan that lay beside the carriage-road.

—Georgette Heyer, The Grand Sophy, chap. 5

My old print Oxford doesn’t have anything for tan in this context, but Webster II has

6. A path or track covered with tanbark, as a circus ring.

And for tanbark,

1. Any bark rich in tannin, bruised or cut into small pieces, and used in tanning. Spent tanbark is used for circus rings, race tracks, etc.

the tannin-depleted bark still holding onto some of its chemistry, and thus slow to degrade.

Which perhaps explains why so many parks feature a Tanbark Trail.