Oscar moved back and forth (6)
I believe the answer is:
onward
'forth' is the definition.
(synonyms)
'oscar moved back' is the wordplay.
'oscar' becomes 'O' (phonetic alphabet: alpha, bravo, charlie etc.).
'moved' becomes 'drawn' (drawing is a kind of moving).
'back' shows that the letters should be reversed in order.
'drawn' written backwards gives 'nward'.
'o'+'nward'='ONWARD'
'and' acts as a link.
(Other definitions for onward that I've seen before include "In a forward direction" , "Forward in time" , "progressive" , "With advancing motion" , "In front" .)