Odd parts of clue they found endearing (4)
I believe the answer is:
cute
'endearing' is the definition.
(I've seen this before)
'odd parts of clue they' is the wordplay.
'odd parts of' indicates alternate letters.
'clue'+'they'='cluethey'
The alternating letters of 'cluethey' are 'CUTE'.
'found' is the link.
(Other definitions for cute that I've seen before include "Quaintly attractive" , "Appealing -- cunning" , "Smart" , "Sweet, attractive" , "Attractive or ingenious" .)