Both Uses of

influential
in
The Scarlet Letter

Had it been otherwise—had an active politician been put into this influential post, to assume the easy task of making head against a Whig Collector, whose infirmities withheld him from the personal administration of his office—hardly a man of the old corps would have drawn the breath of official life within a month after the exterminating angel had come up the Custom-House steps.†
p. 15.0 *

influential = having influence (affecting people or events)

Hester Prynne went one day to the mansion of Governor Bellingham, with a pair of gloves which she had fringed and embroidered to his order, and which were to be worn on some great occasion of state; for, though the chances of a popular election had caused this former ruler to descend a step or two from the highest rank, he still held an honourable and influential place among the colonial magistracy.†
p. 93.2

Definition:

having influence (the ability to affect people or events) -- especially due to respect or admiration