Encourage boy to keep up looking left and right (4,2)
I believe the answer is:
spur on
'encourage' is the definition.
(I know that encourage can be written as spur on)
'boy to keep up looking left and right' is the wordplay.
'boy' becomes 'son' (synonyms).
'to keep' means one lot of letters goes inside another.
'looking left' says the letters should be written in reverse (letters go right to left).
'and' is a charade indicator (letters next to each other).
'right' becomes 'r' (common abbreviation).
'up' backwards is 'pu'.
'pu'+'r'='pur'
'son' placed around 'pur' is 'SPUR ON'.
(Another definition for spur on that I've seen is " Encourage".)