Number wait, losing heart, for official (6)
I believe the answer is:
notary
'for official' is the definition.
(notary is a kind of official)
'number wait losing heart' is the wordplay.
'number' becomes 'no' (abbreviation).
'wait' becomes 'tarry' (to tarry is to wait or linger).
'losing heart' says to hollow out the word (remove centre letters).
'tarry' with its centre taken out is 'tary'.
'no'+'tary'='NOTARY'
(Other definitions for notary that I've seen before include "Person who may certify legal documents" , "Person authorised to certify legal documents" , "One legally empowered to witness signatures and certify documents" , "Official authorised to witness document signing" , "One drawing up legal documents" .)