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29a Mathematical computation, hard stuff (8)
Calculus? I can see 'callus' in there for 'hard stuff' but that leaves two letters unaccounted for.

56a When Westminster quietens, that keeps the wet lot on edge (5,6)
Silly Season. Can't parse the second part of the clue.

1d Fastener joins deer and baby animal up (6)
Buckle? Buck = deer, but what's the baby animal?

1 D Cub is the baby animal and 'up means it becomes Buc. The deer is Elk, also reversed, upwards. Buc kle.

29 A double definition - Calculus is a mathematical computation and also hard stuff (Chambers defines it as 'the mixture of plaque and saliva that forms a hard brownish-yellow layer on the teeth, tartar'.)

Thanks Malone.

56 YON (that) keeping SEAS (the wet lot) on SILL (edge)

Thanks Jono, that was way too contrived for me.