Let everyone down, ignoring outsiders (5)
I believe the answer is:
allow
'let' is the definition.
('allow' can be a synonym of 'let')
'everyone down ignoring outsiders' is the wordplay.
'everyone' becomes 'all' (I've seen this before).
'ignoring outsiders' says to take the centre.
The centre of 'down' is 'ow'.
'all'+'ow'='ALLOW'
(Other definitions for allow that I've seen before include "Acknowledge - concede" , "OK" , "Permit or acknowledge" , "Permit or agree" , "Permit or concede" .)