Closes teen's desk, ignoring odd letters (4)
I believe the answer is:
ends
'closes' is the definition.
(close can mean the end of something)
'teen's desk ignoring odd letters' is the wordplay.
'ignoring odd letters' means one should take alternating letters (letters in odd-numbered positions are removed).
'teens'+'desk'='teensdesk'
The alternate letters of 'teensdesk' are 'ENDS'.
(Other definitions for ends that I've seen before include "See 8" , "Poles, aims" , "Objectives, purposes" , "ambitions" , "Some bowling" .)