A seat on the side, possibly (6)

I believe the answer is:

saddle

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'a seat' is the definition.
(I know that saddle is a type of seat)

I don't understand how the rest of the clue works.

(Other definitions for saddle that I've seen before include "Butcher's cut from the back of an animal" , "Leathery" , "Seat for a rider, horse or bicycle" , "A horseman's seat" , "Lumber (with); one on horse" .)

I've seen this clue in the Evening Standard.

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