Possible Clues:

• Unthink-ing
• That chap's around Leeds, unexpectedly incautious
• Without caution
• Incautious journalist not so taken with governor
• Indifferent hypodermics (new) replaced by hospital on basis of infectiousness
• The man's taken round Leeds, unfortunately paying no attention
• Hospital eradicating first sign of unwanted rash
• Led Hesse (anag)
• He's going around Leeds, surprisingly incautious
• Reckless, careless