I came across this use of the word instant in the Dryden translation of Plutarch's life of Timoleon (who I must admit I'd never heard of before):

But through the care and diligence of his friends, who were very instant with him, and added force to their entreaties, he came to resolve and promise at last, that he would endure living, provided it might be in solitude, and remote from company; so that, quitting all civil transactions and commerce with the world, for a long while after his first retirement he never came into Corinth, but wandered up and down the fields, full of anxious and tormenting thoughts, and spent his time in desert places, at the farthest distance from society and human intercourse.

My dictionary does give "urgent, pressing" as one meaning of instant, but it's not a meaning I am familiar with.

Bingley

Bingley