Look up to observe (4)
I believe the answer is:
keep
'observe' is the definition.
('keep' can be a synonym of 'observe')
'look up' is the wordplay.
'look' becomes 'peek' (peek is a kind of look).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'peek' reversed gives 'KEEP'.
'to' acts as a link.
(Other definitions for keep that I've seen before include "Retain, maintain" , "Look after" , "Hold - fortress" , "Board and lodgings, perhaps" , "Retain in old castle (4)" .)