A sense of the odd slingshot (5)
I believe the answer is:
sight
'a sense' is the definition.
(sight or vision is a sense)
'the odd slingshot' is the wordplay.
'the odd' means one should take alternating letters.
The alternate letters of 'slingshot' are 'SIGHT'.
'of' acts as a link.
(Other definitions for sight that I've seen before include "Bodily faculty" , "Sense" , "24" , "Aiming device on gun" , "Visual perception" .)