Cast Lloyd Bridges right after western knowing ... (7)
I believe the answer is:
worldly
'knowing' is the definition.
(synonyms)
'cast lloyd bridges right after western' is the wordplay.
'cast' indicates an anagram (letters are dispersed or cast around).
'bridges' indicates putting letters inside (some letters go around or bridge others).
'right' becomes 'r' (common abbreviation).
'after' says to put letters next to each other.
'western' becomes 'w'.
'lloyd' with letters rearranged gives 'oldly'.
'oldly' going around 'r' is 'orldly'.
'orldly' after 'w' is 'WORLDLY'.
(Other definitions for worldly that I've seen before include "Material; experienced" , "Global" , "Concerned with material things" , "Earthly - experienced" , "Materialistic" .)