Observed a number losing heart (4)
I believe the answer is:
seen
'observed' is the definition.
('seen' can be a synonym of 'observed')
'a number losing heart' is the wordplay.
'a number' becomes 'seven' (seven is a kind of number).
'losing heart' means to remove the middle letters.
'seven' with its centre taken out is 'SEEN'.
(Other definitions for seen that I've seen before include "Distinguished" , "Perceived by sight" , "Spotted" , "Noticed" , "watched" .)