10001000 teachers might be kind of shy (7)
I believe the answer is:
coconut
'kind of shy' is the definition.
(coconut shy is a traditional game)
'10001000 teachers' is the wordplay.
'10001000' becomes 'coco' (c is roman numeral for 100 c0c0).
'teachers' becomes 'nut' (National Union of Teachers).
'coco'+'nut'='COCONUT'
'might be' is the link.
(Other definitions for coconut that I've seen before include "Large palm fruit" , "Fruit at which to shy" , "Shy occupier" , "fair target" , "that's hairy and tough!" .)