Sense shown by head of security in gallery (5)
I believe the answer is:
taste
'sense' is the definition.
(taste is a kind of sense)
'head of security in gallery' is the wordplay.
'head of' suggests taking the first letters.
'in' indicates putting letters inside.
'gallery' becomes 'tate' (I've seen this before).
The initial letter of 'security' is 's'.
's' inserted within 'tate' is 'TASTE'.
'shown by' is the link.
(Other definitions for taste that I've seen before include "style" , "Smack" , "Impression from food" , "The ability to discern good quality" , "Sip" .)