Runny nose perhaps picked up in chamber (5)
I believe the answer is:
rheum
'runny nose' is the definition.
(I've seen this before)
'picked up in chamber' is the wordplay.
'picked up in' shows a homophone (sound like).
'chamber' becomes 'room' (I've seen this before).
'room' is a homophone of 'RHEUM'.
'perhaps' is the link.
(Other definitions for rheum that I've seen before include "Watery mucous discharge" , "nasal discharge" , "that's rather snotty?" , "Watery discharge; sounds like space" , "cold once upon a time" .)