、。
I'll drop you a line as soon as I arrive in Hokkaido.
Literal
Hokkaido [to-に] arrive-as-soon-as, a-note give-[humble-差し上げる].
次第 after a verb stem (着き次第) means 'as soon as [verb].' 一筆 ('a line, a short note') literally 'one brush[stroke].' 差し上げる is the humble form of あげる ('to give [to higher status]') — extremely polite. The whole sentence is formal/literary, suitable for a polite letter or respectful communication.