Possible Clues:

• Continuation
• Investigate further, and what the starts of the starred clues' answers can do?
• Sequel
• Investigate something further
• Almost achieve backing to pen old Western sequel
• Further monitoring of hit-maker's next record
• Pursue to a conclusion
• Subsequent examination of dog at an end
• Further examination makes half-hearted fool depressed at university
• Work building on an earlier one