Possible Clues:

• A new job, loading a galleon initially, in port
• Northern city has an unpleasant duty collecting silver
• On a charge, drunk in port
• On a charge, being drunk in port
• "... the bay/ From whence at first she weigh'd her —" (Titus Andronicus)
• The era for television presenter perhaps in Alaska
• TV presenter in the US has time in a state's largest city
• An unpleasant duty impounding silver in Alaska
• City at the head of Cook Inlet