Learning to look about (4)
I believe the answer is:
lore
'learning' is the definition.
(both can mean tradition or knowledge)
'look about' is the wordplay.
'look' becomes 'lo' ('lo' is an archaic exclamation meaning 'look!').
'about' becomes 're' ('re' means regarding or about).
'lo'+'re'='LORE'
'to' acts as a link.
(Other definitions for lore that I've seen before include "Folk knowledge" , "Ancient learning" , "Old learning" , "Tales of old" , "old-fashioned thong" .)