You and I exist incompletely and deteriorate (4)
I believe the answer is:
wear
'deteriorate' is the definition.
(wear can mean to deteriorate over time)
'you and i exist incompletely' is the wordplay.
'you and i' becomes 'we'.
'exist' becomes 'are' ('they exist' means 'they are').
'incompletely' means to remove the last letter.
'are' with its final letter taken off is 'ar'.
'we'+'ar'='WEAR'
'and' is the link.
(Other definitions for wear that I've seen before include "Damage from use" , "Tolerate" , "(Put on) clothing" , "Northern river - sport" , "Durham's river - erosion" .)