Both Uses of

succession

in

All's Well That Ends Well

—Beware of them, Diana; their promises, enticements, oaths, tokens, and all these engines of lust, are not the things they go under; many a maid hath been seduced by them; and the misery is, example, that so terrible shows in the wreck of maidenhood, cannot for all that dissuade succession, but that they are limed with the twigs that threaten them.
Scene 3.5 (definition 1) *

succession = replacement (other women replacing those who had previously seduced)

Sir, for a quart d'ecu he will sell the fee-simple of his salvation, the inheritance of it; and cut the entail from all remainders and a perpetual succession for it perpetually.
Scene 4.3 (definition 2) *

succession = repetition for a line of descendants (one after another)

Definitions:

(1) (succession as in: presidential line of succession)
replacement -- especially someone to taking a job or position after another leaves it

(2) (succession as in: a succession of events)
series or sequence (one after another)