Leaders of Senate have ordered witness to appear (4)
I believe the answer is:
show
'appear' is the definition.
(showing is a kind of appearing)
'leaders of senate have ordered witness' is the wordplay.
'leaders of' suggests taking the first letters.
The initial letters of 'senate have ordered witness' is 'SHOW'.
'to' is the link.
(Other definitions for show that I've seen before include "Demonstrate; spectacle" , "Exhibit - present" , "event" , "Demonstrate or reveal" , "Expose" .)