Nerve cells that could make nose run (7)
I believe the answer is:
neurons
'nerve cells' is the definition.
('neuron' can be a synonym of 'nerve cell')
'could make nose run' is the wordplay.
'could make' is an anagram indicator.
'nose'+'run'='noserun'
'noserun' anagrammed gives 'NEURONS'.
'that' is the link.
(Other definitions for neurons that I've seen before include "They conduct nerve impulses" , "Nerve cells" .)