Possible Clues:

• Nocturnal bloodsucker
• Bloodsucker found in the garden?
• Insect in the mattress, perhaps?
• One is a sucker for those that are lying
• Bloodsucking parasite listens as you sleep perhaps
• Bloodsucker in the garden is planted by three-quarters of 29 across
• Night-time biter
• Teacher with listening device — unwelcome companion between the sheets
• Teacher with complaint or problem after retiring
• Here you can drop off surveillance device, sucker!