Identity of nurse stopping runny noses (7)
I believe the answer is:
oneness
'identity' is the definition.
(oneness is a kind of identity)
'nurse stopping runny noses' is the wordplay.
'nurse' becomes 'EN' (abbreviation for enrolled nurse).
'stopping' is an insertion indicator (inserted letters stop or plug a gap).
'runny' indicates an anagram (I've seen this in other clues).
'noses' anagrammed gives 'oness'.
'en' put into 'oness' is 'ONENESS'.
'of' acts as a link.
(Other definitions for oneness that I've seen before include "Singular quality" , "Uniqueness" , "Agreement" , "singularity" , "Unified state" .)